I think Lennie is dependent on George, because he knows that George is only doing what he thinks is best to help Lennie, when no one else would. There's a possibility they're connected through family, but I'm not sure. Lennie's probably found that he can't live very well on his own and noticed that George is willing to help. Fairly simple.
George keeps Lennie around because he knows the guy probably wouldn't be able to live on his own. They're probably pretty good friends by now, anyway, so George has no reason to let him go. Though, he might just use Lennie for his strength so he can get jobs done without working, which is probably what's going to happen, due to the way George spoke to Lennie about their next job.
