In Of Mice and Men by John Steinbeck, how does Lennie make sacrifices for George?

Lennie is devoted to George and would undoubtedly like to make sacrifices for him and be able to do more for him, but Lennie is relatively powerless because of his mental handicap. There are a couple of instances in which he shows he would make a sacrifice if he could. In the opening chapter when Lennie prompts George's tirade by saying he likes beans with his ketchup, Lennie listens to George's verbal abuse occasioned by his pent-up anger and frustration. Lennie then gently says,

I was only foolin', George. I don't want no ketchup. I wouldn't eat no ketchup if it was right here beside me.

George feels a little ashamed of himself. He says,

If it was here, you could have some.

Lennie continues,

But I wouldn't eat none, George. I'd leave it all for you. You could cover your beans with it and I wouldn't touch none of it.

Poor Lennie, who has nothing to give his friend, tries to give him a whole bottle of imaginary ketchup.
In the same chapter, Lennie asks,

George, you want I should go away and leave you alone?. . . Well, I could. I could go off in the hills there. Someplace I'd find a cave. . . If you don't want me I can go off in the hills an' find a cave. I can go away any time.

In the very last chapter, just before George kills him, Lennie repeats his offer to go away and live in a cave. He knows he is a burden and would even sacrifice his life for his friend by living like a wild animal before he died of exposure or starvation. Lennie's kind heart makes him the most memorable and well-liked character in this book. Many readers remember Of Mice and Men mainly because of Lennie Small.