Lennie has a mental disabilty which is a conflict between him and George, since George does not have so much patience. Lennie wants to run away to a cave so that he won't bother George. And he believes if he runs aways he will be happier and have all the mice he wants, but George does not let him.
George always seems mad or upset. The conflict between him and Lennie is that even though he wishes Lennie to be gone, he really does't mean it. Deep inside, George cares about Lennie.
George always screams at Lennie, because he wants to get a job, and is tired of being punished for Lennie's actions. This makes Lennie very sad and upset which makes him rethink about running away. George should let Lennie at least talk a little or speak for himself, or else it could become a conflict for their job, later in the story.