Doughty means "brave and persistent". At bay means "Forced to face or confront one's attackers or pursuers; cornered."
The meaning of "killing nothing" would be clear; but instead of absolutely "nothing", Tolkien writes "nothing that lived": in other words, they do not kill anything that is alive. (This is actually a pleonasm, since if you kill something it must be something that lives, but presumably it's written that way for poetic effect.)
A rephrasing of the sentence in simpler language might be:
They would rarely argue, and never killed living things for sport, but they were brave when cornered, and could still use weapons if necessary.