Which sentence is better?

He had to lay down his life.

The normal form in British English is:  "He laid down his life."  With the meaning that he sacrificed his own life for the sake of his friends, his family, his country, etc.  Note lack of "He had to"

Neither of your sentences is natural.

Oof.  If he sacrificed himself for some reason, then he could be said to have laid his life down; and perhaps that he had to lay his life down, although the idea of laying down my life is, of itself, a choice and therefore voluntary so not actually something I would ever really and truly HAVE to do.  If I cannot refuse to give up my life (there is no choice), then I am not laying it down, I am being murdered: the other is killing me rather than I am dying for a cause.

People do not usually talk about putting down their own life or talk about self-sacrifice of life as "putting down".  Putting down is a euphemism for killing a sick pet or severely injured animal.  We only rarely even consider the death of a human as a "putting down" of his life, and only then, sometimes, when we talk about people we do not consider as being human in any real way, but only as animals (subhuman; criminal and evil).