They both need a friend too. By the time you get to chapters 4-5, George leaves for the night and Crooks teases Lennie about George leaving him for good. Lennie knows George would never do that and Crooks discusses what it is like to be lonely. These guys both need each other for companionship. In fact, if you look at every other character, they are longing for relationship. It kills Candy to loose his dog. Curley and his wife have an empty marriage, Crooks is an outcast. The need for relationship is all over this book. This is what makes the end so difficult to grasp. Even though George gets relieved by having the responsibility for Lennie's actions over, he is hurt that he will not be able to have his friend anymore.

I think that it is easier to see why Lennie needs George than to see why George needs Lennie.

Lennie needs George for two reasons.  First, he needs George to keep him out of trouble.  Without George, Lennie is not really intelligent enough to make his own way in the world.  Second, he needs George to give him a dream to live for.  Lennie is probably not capable of making up his own dream and having a clear vision of that dream.

I think George needs Lennie because caring for Lennie makes him feel useful and important.  George does not appear to have that much going for him and I think that having someone who depends on him makes him feel like he is special to someone and that someone needs him.