Lennie threatens to leave George because George makes Lennie feel like he is a burden. George can't have a girlfriend. George has to have the life of a traveling laborer because wherever they go Lennie gets in trouble. Lennie has the needs of a child like needing ketchup to go with his beans. Lennie plays with soft dead animals because he likes how they feel even though they aren't healthy for him to play with. Finally, Lennie says that he can go and live off in a cave somewhere by himself and be just fine.
Lennie does this with intention. He knows it will make George feel guilty. He knows George will never make him follow through with it. But on the one hand, it is at least sweet that Lennie offers because he does quite effectively drain George of his life. George can barely leave Lennie's side.
Here is a good quote to use:
Lennie avoided the bait. He had sensed his advantage. "If you don't want me, you only jus' got to say so, and I'll go off in those hills right there -"