Angie Hobbs, a University of Warwick fellow who "has written widely on the philosophical history of friendship," discusses Plato's Lysis:
[Socrates, Lysis, Menexenus, and Hippothales] examine a variety of models for why individuals form friendships. The protagonists consider the idea of like being attracted to like,which is a pre-Socratic idea from Empedocles, but reject it on thegrounds that such a friendship would produce too much competition andrivalry. They wonder about the Heraclitian view that oppositesattract—which was a popular proverb for the ancient Greeks, as it isfor us—but throw that out on the grounds that it would mean that thegood is attracted to the bad, or the just to the unjust, and that can’tbe the case. The model to which they appear most sympathetic is that offriendship between two good people—not because they are alike, butbecause they are attracted to each other’s goodness.
The best kind offriendship isn’t based on utility or pleasure or some particular end,but on appreciation of the other’s goodness, which reflects your owngoodness. This is not entirely conclusive, because questions aboutself-sufficiency linger in the air—do truly good people really needfriends? Are they not self-sufficient? This is a problem if friendshipis viewed as simply filling a lack, like food or drink. These questionsare not entirely resolved, and are complicated still further if we aresupposed to be trying to imitate God: surely God has no need offriends.