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 the grounds that such a friendship would produce too much competition and rivalry. They wonder about the Heraclitian view that opposites attractwhich was a popular proverb for the ancient Greeks, as it is for usbut throw that out on the grounds that it would mean that the good is attracted to the bad, or the just to the unjust, and that can’t be the case. The model to which they appear most sympathetic is that of friendship between two good peoplenot because they are alike, but because they are attracted to each other’s goodness.
The best kind of friendship isn’t based on utility or pleasure or some particular end, but on appreciation of the other’s goodness, which reflects your own goodness. This is not entirely conclusive, because questions about self-sufficiency linger in the airdo truly good people really need friends? Are they not self-sufficient? This is a problem if friendship is viewed as simply filling a lack, like food or drink. These questions are not entirely resolved, and are complicated still further if we are supposed to be trying to imitate God: surely God has no need of friends.?