Perhaps one could look at these verses this way…
Suppose you are in a battle and your friend is safely tucked behind a tree… occasionally he sends a bullet to the opposing side… finally there is one enemy left… but only you and this one friend are left alive. The enemy throws a grenade at you… and your friend leaps out from behind the tree, grabs the grenade, and runs straight at the enemy. The grenade explodes and he dies, but he was far enough away that you are not killed, though perhaps a bit of shrapnel got in your skin.
You might go home and tell stories of how that friend “laid down his life…” did he commit suicide? Perhaps in a way he did, because he knew he would die when he ran with that grenade. But it was not his intention to kill himself to end his misery or something like that, it was rather to save your life. Furthermore, you would be right to say that the enemy killed your friend… but that your friend laid down his life as well–because perhaps one might say the enemy never would have killed your friend if your friend hadn’t let himself be killed–for your sake. Dunno if that helps, but it might be a way to look at it.
There needn’t be a dichotomy between “laying down your life” and someone killing you.