Let us consider the following verses which were rendered in the English as "lay down...life". 

John 15:13-15 
13 Greater love hath no man than this, that a man lay down his life for his friends. 
14 Ye are my friends, if ye do whatsoever I command you. 
15 Henceforth I call you not servants; for the servant knoweth not what his lord doeth: but I have called you friends; for all things that I have heard of my Father I have made known unto you. (KJV) 

John 10:15-18 
15 As the Father knoweth me, even so know I the Father: and I lay down my life for the sheep. 
16 And other sheep I have, which are not of this fold: them also I must bring, and they shall hear my voice; and there shall be one fold, and one shepherd. 
17 Therefore doth my Father love me, because I lay down my life, that I might take it again. 
18 No man taketh it from me, but I lay it down of myself. I have power to lay it down, and I have power to take it again. This commandment have I received of my Father. (KJV) 

John 13:37-38 
37 Peter said unto him, Lord, why cannot I follow thee now? I will lay down my life for thy sake. 
38 Jesus answered him, Wilt thou lay down thy life for my sake? Verily, verily, I say unto thee, The cock shall not crow, till thou hast denied me thrice. (KJV) 

I Jn 3:16-24 
16 Hereby perceive we the love of God, because he laid down his life for us: and we ought to lay down our lives for the brethren. 
17 But whoso hath this world's good, and seeth his brother have need, and shutteth up his bowels of compassion from him, how dwelleth the love of God in him? 
18 My little children, let us not love in word, neither in tongue; but in deed and in truth. 
19 And hereby we know that we are of the truth, and shall assure our hearts before him. 
20 For if our heart condemn us, God is greater than our heart, and knoweth all things. 
21 Beloved, if our heart condemn us not, then have we confidence toward God. 
22 And whatsoever we ask, we receive of him, because we keep his commandments, and do those things that are pleasing in his sight. 
23 And this is his commandment, That we should believe on the name of his Son Jesus Christ, and love one another, as he gave us commandment. 
24 And he that keepeth his commandments dwelleth in him, and he in him. And hereby we know that he abideth in us, by the Spirit which he hath given us. (KJV) 

"lay down" 
5087 tithemi (tith'-ay-mee); 
a prolonged form of a primary theo (theh'-o) (which is used only as alternate in certain tenses); to place (in the widest application, literally and figuratively; properly, in a passive or horizontal posture, and thus different from 2476, which properly denotes an upright and active position, while 2749 is properly reflexive and utterly prostrate): 
KJV-- + advise, appoint, bow, commit, conceive, give, X kneel down, lay (aside, down, up), make, ordain, purpose, put, set (forth), settle, sink down. 

5087 tithemi- 
1) to set, to put, to place 
a) to place or to lay 
b) to put down, to lay down 
1) to bend down 
2) to lay off or aside, to wear or to carry no longer 
3) to lay by, to lay aside money 
c) to set on (serve) something to eat or to drink 
d) to set forth, something to be explained by discourse 
2) to make; to make (or set) for oneself or for one's use 
3) to set, to fix establish 
a) to set forth 
b) to establish, to ordain 

Now, consider some of the verses which utilize the Greek word # 5087 which is "tithemi". 
I have not offered all the verses which utilize "tithemi", because there are simply way too many, but I think these verses show all the various English language renderings of "tithemi". 

Matt 12:18 
18 Behold my servant, whom I have chosen; my beloved, in whom my soul is well pleased: I will put my spirit upon him, and he shall shew judgment to the Gentiles. (KJV) 

Matt 22:44 
44 The LORD said unto my Lord, Sit thou on my right hand, till I make thine enemies thy footstool? (KJV) 

Matt 24:51 
51 And shall cut him asunder, and appoint him his portion with the hypocrites: there shall be weeping and gnashing of teeth.  (KJV) 

Mark 4:30 
30 And he said, Whereunto shall we liken the kingdom of God? or with what comparison shall we compare it? (KJV) 

Mark 6:29 
29 And when his disciples heard of it, they came and took up his corpse, and laid it in a tomb. (KJV) 

Mark 15:19 
19 And they smote him on the head with a reed, and did spit upon him, and bowing their knees worshipped him. (KJV) 

Luke 9:44 
44 Let these sayings sink down into your ears: for the Son of man shall be delivered into the hands of men. (KJV) 

Acts 5:4 
4 Whiles it remained, was it not thine own? and after it was sold, was it not in thine own power? why hast thou conceived this thing in thine heart? thou hast not lied unto men, but unto God. (KJV) 

Acts 5:15 
15 Insomuch that they brought forth the sick into the streets, and laid them on beds and couches, that at the least the shadow of Peter passing by might overshadow some of them. (KJV) 

Acts 5:18 
18 And laid their hands on the apostles, and put them in the common prison. (KJV) 

Acts 5:25 
25 Then came one and told them, saying, Behold, the men whom ye put in prison are standing in the temple, and teaching the people. (KJV) 

Acts 7:16 
16 And were carried over into Sychem, and laid in the sepulchre that Abraham bought for a sum of money of the sons of Emmor the father of Sychem. (KJV) 

Acts 7:60 
60 And he kneeled down, and cried with a loud voice, Lord, lay not this sin to their charge. And when he had said this, he fell asleep. (KJV) 

Acts 9:37 
37 And it came to pass in those days, that she was sick, and died: whom when they had washed, they laid her in an upper chamber. (KJV) 

Acts 9:40 
40 But Peter put them all forth, and kneeled down, and prayed; and turning him to the body said, Tabitha, arise. And she opened her eyes: and when she saw Peter, she sat up. (KJV) 

Acts 12:4 
4 And when he had apprehended him, he put him in prison, and delivered him to four quaternions of soldiers to keep him; intending after Easter to bring him forth to the people. (KJV) 

Acts 13:29 
29 And when they had fulfilled all that was written of him, they took him down from the tree, and laid him in a sepulchre.  (KJV) 

Acts 13:47 
47 For so hath the Lord commanded us, saying, I have set thee to be a light of the Gentiles, that thou shouldest be for salvation unto the ends of the earth. (KJV) 

Acts 19:21 
21 After these things were ended, Paul purposed in the spirit, when he had passed through Macedonia and Achaia, to go to Jerusalem, saying, After I have been there, I must also see Rome. (KJV) 

Acts 20:28 
28 Take heed therefore unto yourselves, and to all the flock, over the which the Holy Ghost hath made you overseers, to feed the church of God, which he hath purchased with his own blood. (KJV) 

Acts 20:36 
36 And when he had thus spoken, he kneeled down, and prayed with them all. (KJV) 

Acts 21:5 
5 And when we had accomplished those days, we departed and went our way; and they all brought us on our way, with wives and children, till we were out of the city: and we kneeled down on the shore, and prayed. (KJV) 

Acts 27:12 
12 And because the haven was not commodious to winter in, the more part advised to depart thence also, if by any means they might attain to Phenice, and there to winter; which is an haven of Crete, and lieth toward the south west and north west.  (KJV) 

Rom 4:17 
17 (As it is written, I have made thee a father of many nations,) before him whom he believed, even God, who quickeneth the dead, and calleth those things which be not as though they were. (KJV) 

Rom 9:33 
33 As it is written, Behold, I lay in Sion a stumblingstone and rock of offence: and whosoever believeth on him shall not be ashamed. (KJV) 

Rom 14:13 
13 Let us not therefore judge one another any more: but judge this rather, that no man put a stumblingblock or an occasion to fall in his brother's way. (KJV) 

1 Cor 3:10 
10 According to the grace of God which is given unto me, as a wise masterbuilder, I have laid the foundation, and another buildeth thereon. But let every man take heed how he buildeth thereupon. (KJV) 

1 Cor 3:11 
11 For other foundation can no man lay than that is laid, which is Jesus Christ. (KJV) 

1 Cor 9:18 
18 What is my reward then? Verily that, when I preach the gospel, I may make the gospel of Christ without charge, that I abuse not my power in the gospel. (KJV) 

1 Cor 12:18 
18 But now hath God set the members every one of them in the body, as it hath pleased him. (KJV) 

1 Cor 12:28 
28 And God hath set some in the church, first apostles, secondarily prophets, thirdly teachers, after that miracles, then gifts of healings, helps, governments, diversities of tongues. (KJV) 

1 Cor 15:25 
25 For he must reign, till he hath put all enemies under his feet. (KJV) 

1 Cor 16:2 
2 Upon the first day of the week let every one of you lay by him in store, as God hath prospered him, that there be no gatherings when I come. (KJV) 

2 Cor 3:13 
13 And not as Moses, which put a vail over his face, that the children of Israel could not stedfastly look to the end of that which is abolished: (KJV) 

2 Cor 5:19 
19 To wit, that God was in Christ, reconciling the world unto himself, not imputing their trespasses unto them; and hath committed unto us the word of reconciliation. (KJV) 

1Thes 5:9 
9 For God hath not appointed us to wrath, but to obtain salvation by our Lord Jesus Christ, (KJV) 

1 Tim 1:12 
12 And I thank Christ Jesus our Lord, who hath enabled me, for that he counted me faithful, putting me into the ministry;  (KJV) 

1 Tim 2:7 
7 Whereunto I am ordained a preacher, and an apostle, (I speak the truth in Christ, and lie not;) a teacher of the Gentiles in faith and verity. (KJV) 

2 Tim 1:11 
11 Whereunto I am appointed a preacher, and an apostle, and a teacher of the Gentiles. (KJV) 

Heb 1:2 
2 Hath in these last days spoken unto us by his Son, whom he hath appointed heir of all things, by whom also he made the worlds; (KJV) 

Heb 1:13 
13 But to which of the angels said he at any time, Sit on my right hand, until I make thine enemies thy footstool? (KJV) 

Heb 10:13 
13 From henceforth expecting till his enemies be made his footstool. (KJV) 

1 Pet 2:6 
6 Wherefore also it is contained in the scripture, Behold, I lay in Sion a chief corner stone, elect, precious: and he that believeth on him shall not be confounded. (KJV) 

1 Pet 2:8 
8 And a stone of stumbling, and a rock of offence, even to them which stumble at the word, being disobedient: whereunto also they were appointed. (KJV) 

I Jn 3:16 
16 Hereby perceive we the love of God, because he laid down his life for us: and we ought to lay down our lives for the brethren. (KJV) 

Rev 1:17 
17 And when I saw him, I fell at his feet as dead. And he laid his right hand upon me, saying unto me, Fear not; I am the first and the last: (KJV) 

Rev 10:2 
2 And he had in his hand a little book open: and he set his right foot upon the sea, and his left foot on the earth, (KJV) 

Rev 11:9 
9 And they of the people and kindreds and tongues and nations shall see their dead bodies three days and an half, and shall not suffer their dead bodies to be put in graves. (KJV) 

What does this word "tithemi" speak of? 
"will put", "putting", "to be put", 
"I make", "be made", "I may make" 
"appoint", "am appointed" , "he hath appointed", "they were appointed" 
"am ordained" 
"advised", 
"kneeled down", "we kneeled down" 
"hath set", "he set" 
"hath committed" 
"sink down" 
"bowing" 
"shall we compare it" 
"purposed" 
"lay down", "laid", "let lay" 

"Greater love hath no man than this, that a man lay down his life for his friends" 
Now let us look at the word "life" from the phrase "lay down his life". 
5590 psuche (psoo-khay'); 
from 5594; breath, i.e. (by implication) spirit, abstractly or concretely (the animal sentient principle only; thus distinguished on the one hand from 4151, which is the rational and immortal soul; and on the other from 2222, which is mere vitality, even of plants: these terms thus exactly correspond respectively to the Hebrew 5315, 7307 and 2416): 
KJV-- heart (+-ily), life, mind, soul, + us, + you. 

5590 psuche- 
1) breath 
a) the breath of life: the vital force which animates the body and shows itself in breathing: 
1) used of animals 
2) used of men 
b) life 
c) that in which there is life, a living being, a living soul 
2) the soul 
a) the seat of the feelings, desires, affections, aversions (our heart, soul, etc.) 
b) the (human) soul insofar as it is constituted that by the right use of the aids offered it by God it can attain its highest end and secure eternal blessedness, the soul regarded as a moral being designed for everlasting life 
c) the soul as an essence which differs from the body and is not dissolved by death (distinguished from other parts of the body) 

Does this help in understanding the phrase "lay down his life for his friends"? 
It does not indicate 'death', but refers to a giving of one's self (feelings, desires, affections, aversions (our heart, soul, etc.)) for the benefit of others. 
YAHSHUA'S friends and some of YHVH'S servants shall suffer the indignation, scorn, ridicule and other indignities for the benefit of YHVH'S children, in order to have YHVH'S Truth published unto the world.