Steinbeck presents the relationship shared between Lennie and George as being similar to a "caretaker" relationship. An argument can be made that the relationship is not only similar to a "caretaker" relationship, but is actually a relationship of that type.
George explains that he agreed to take care of Lennie after Lennie's Aunt Clara died.
We see Lennie from the outset of the novel as being childlike and innocent, yet he also has a tendency to get into trouble. The pair have been "run out of weed" where Lennie got into trouble. He needs to be taken care of, protected from harm, from starvation, and from the law as well (when he gets into trouble).
Beyond the dynamic between the two characters, the relationship they share is also presented as being both intimate and historic.
George and Lennie have known each other for a long time and they know each other well. We see this when Lennie tries to trick George at the beginning of the book (by retrieving the mouse) and George immediately penetrates Lennie's deception.
There is also a great loyalty between George and Lennie, seen when Crooks suggests to Lennie that something bad may have happened to George in town. Lennie grows quickly upset and begins to threaten violence to Crooks and to anyone who would dare even "talk harm" to George.
Finally, this friendship is complicated and it compromises both men to some extent. Lennie sacrifices some of his desires in order to please George and George sacrifices quite a bit of freedom due to his role as Lennie's caretaker.