“Steve Trevor is an American spy whose life pursuit is to prevent people from dying by a lethal weapon” sembra naturale?

Since this actually has a context I would not use weaponS and since that's on the plot of Wonder Woman (which I believe that is a poisonous gas ,if my memory isn't failing me at the moment) I highly recommend you to remain using the singular form of the noun .

Ps: I've used this marks"{...}" to present you a suggestion, just ending there is okay (or changing to something on the lines of "mission is to save people by ending the war". But it depends a lot on what idea you are trying to convey.

As dracoboy suggests, you should specify what the lethal weapon is in this clause. If you specified it in the previous clause, you can say “from this lethal weapon.” In English, generally speaking, the more context there is, the better.

You may choose to replace “spy” with “agent”, as I think that sounds a bit more formal/academic. “Operative” is another option.

Also, “pursuit” is fine. It sounds better than “mission” to my ears. Using “Assignment” or “task” makes it seem like he doesn’t have any personal stake in whether people die or not; he’s just being ordered to prevent it.