Friendship (philia) is the central focus of the arguments in the Lysis, and love (eros) defines the frame in which these arguments take place. The dialogue begins with Socrates offering to help Hippothales figure out how best to court the boy Lysis, with whom Hippothales is hopelessly in love. Socrates's main objective in this regard is to show Hippothales how to humble Lysis into desiring him as a teacher, rather than by inflating Lysis's ego with praise and thus making him harder to get. None of this can be understood without some basic knowledge about how love relationships between men and boys functioned in Socrates's and Plato's Athens. The key to understanding how these relationships operated lies in the blending of passionate, occasionally physical love with the inspiration given by the ideal beauty of the youth and with the role of the older lover as a teacher of manly ideals and wisdom (see Lover in the terms list for more information). This is the framework for Socrates's conversation with the boys, as Hippothales watches the demonstration from behind a nearby pillar.
Friendship, such as that enjoyed between Lysis and Menexenus, is the topic addressed within this context. Socrates considers a number of hypotheses about friendship, shifting a bit from an attempt to describe what person (or role) is the true friend to trying to find the universal cause of desire. Briefly, the possibilities for defining "what is the friend" include: the lover, the beloved, the like, the unlike, and the good. All are rejected, primarily due to the seemingly intractable problem that like has no reason to befriend like. By the end of the dialogue, a rough model for further investigation seems to have been set up: a true account of friendship has to explain why two people need or desire each other, but cannot allow for "monstrous" possibilities such as the good befriending the bad (or the just the unjust). The trick is to explain desire without allowing it to encompass bizarre or unacceptable situations. In fact, this is precisely the situation with regard to Socrates's attempt to show Hippothales the right way to put his desire for Lysis into effect. Thus, friendship and desire end up sharing a common ground in questions of desire.
Questions about likeness and difference dominate the middle section of the dialogue, and yield a dilemma that ultimately frustrates its whole aim. Socrates, borrowing from poets and philosophers, suggests that friendship might be explained by the fact that "God draws like to like." Perhaps likeness is the basis of friendship. It may be more Plato's voice than Socrates that rejects this proposition on the basis of a foundational element in the theory of identity. The problem revolves around the very fundamentals of identity and difference, and is expressed in two ways. First, "like is drawn to like" seems to imply that bad people can be friends to bad people. This seems intuitively wrong to Socrates, since bad people cannot be true friends to anyone in as much as they are bad. Strikingly, however, Socrates frames this objection in terms of a theory of identity: bad people cannot be truly like other people at all, because they are not like themselves—not at harmony with themselves. Thus, inter-personal identity is thwarted by the remarkable quality of intra-personal non-identity. The second way the objection to likeness is expressed is through the objection that the extent to which two people are alike is precisely the extent to which they cannot need or desire anything from each other (because, by definition, they already have it). Thus, two people that are partially alike could still be useful to each other, but their likeness is precisely where they are not. Thus, it cannot be the cause of friendship. This important point aligns desire with difference, and excludes desire completely from identity as such. Toward the end of the dialogue, this exclusion, this objection to "like is drawn to like," will foil Socrates's last attempt to explain the desire that leads to friendship.
As discussed in the entry on "Likeness and Identity" above, desire undergoes some very strict analysis in this dialogue. Most notably, desire is judged to depend on difference rather than on identity. This, however, is precisely what frustrates all of Socrates's attempts to account for desire, since a desire defined only by difference ("unlikeness") would lead to "monstrous" friendships, like the good befriending the evil. Nonetheless, it is striking that all of the twists, turns, and rejections of the Lysis culminate in the one final theory that friendship is simply due to desire. Bound up in this final assertion is the intriguing but underdeveloped quality of the "congenial," which appears to be an attempt to theorize how two things can be different in a harmonious way (this would solve the problem of "monstrously" inharmonious friendships). Unfortunately, the congenial is quickly judged to be little different from the like, and to have the same problems. One other property of desire is asserted in the dialogue: desire, in itself, is neutral, like hunger. It is this property of desire that allows Socrates to throw out evil as the thing that drives people toward the good of friendship; since desire is neutral, it would be around even if all evil disappeared.
The Lysis is notable for the ways in which it weaves erotic desire and friendship into a complex tapestry. Throughout much of the dialogue, the causes of both eros(passionate love) and philia (fondness, friendship) seem to overlap quite a bit precisely on the issue of desire. Desire also binds the context of the dialogue (Hippothales's erotic love for Lysis) to its content (Socrates's discussion of friendship).
The idea that friendship is based in some fundamental way on usefulness may seem surprising if we imagine Plato's Socrates to be a philosopher solely of pure knowledge and virtue. But usefulness often comes into play in the dialogues as a mediator between the abstract virtues that Socrates attempts to construct and the worldly, practical virtues assumed by his interlocutors. This is certainly true in the Lysis, where Socrates has to convince two energetic young boys that knowledge and friendship should supersede goals like owning dogs and horses or driving the family chariot. Thus, Socrates convinces Lysis to strive for knowledge and understanding because these things will make him useful, and so give him greater control over the practical (and fun) elements of his life. In the arguments about friendship, however, use-value seems to play a deeper role, functioning at the very root of love and desire. Specifically, the demand that two friends be "useful" to each other prevents any possibility that likeness can be the cause of friendship (since two people can get nothing from each other to the exact extent that they are the same). Although the various possible causes of friendship include a wide range of qualities over the course of the dialogue, most of them depend at some point on this notion of practical use, a notion that friendship is to some extent a profitable exchange (as with the sick body "befriending" medicine).
The Lysis does not involve any sustained inquiry into the nature of the good (as some of the other dialogues do), but good is suggested as an obvious choice for the quality that motivates friendship. Perhaps, proposes Socrates, the friend is simply the good. It has already been concluded at this point, in the discussion of like befriending like, that evil can be the friend of nobody; since evil is not even like itself (not in harmony with itself), it cannot be like (or in harmony with) anything else. Socrates also seems to take it as a given that evil can never be a friend. The problem with the proposition that the good is the friend is similar to the problem with like befriending like: what is already good has no need of more good, and so its desire for a friend cannot be caused by the desire to improve. Socrates's solution to this problem is ingenious, if a bit awkward. The good cannot be the friend of the good or of the evil, but it could be the friend of that which is neither good nor evil (i.e., the neutral). The solution, then, would be that friendship is caused by the neutral desiring the good because of the presence of evil. Socrates is pleased with this formulation, but it is soon dropped due to an entirely new objection. On this model, it would seem that the neutral loves the good "for the sake of" evil, a situation that would make the cause of friendship contingent on a secondary goal (that of escaping evil). This is not a strong enough cause for Socrates, who wants an ultimate and self-sufficient cause. Thus, he argues that, even if evil completely disappeared, desire, which is itself neither good nor evil, would remain. This means that love and friendship would probably occur regardless of the presence of evil. The Lysis never addresses the lingering question in this area: namely, why can't the neutral be said to love the good regardless of evil?