The strange thing about Lezginka and the various videos of the dance on sites like Youtube, is that there seems to be a war, fought in the comments sections, over whether it is an all male dance, or whether it is a dance that includes one or more women. Some maintain the former, some the latter, and others maintain that the Lezginka includes women, but that there is another all-male dance called the Mkhedruli ("military" in Georgian).
I think the answer is that it's all one dance that went through a historical change. It started out as an all-male war dance, like this scene from the Russian made movie, 12, were a boy dances the Lezginka with Chechen Rebels resting at his fathers farm:
Or, if you'd prefer a more real-life example, consider this clip of Chechens dancing The Lezginka at a party:
There's no doubting that the above dances, whether you want to call them "Lezginka" or Mkhedruli, are all-male war dances. Aside from the fact that the participants are exclusively men, the male aesthetic of the dance is unmistakable. There are no curves in the Lezginka, only elbows and knees in a whirlwind of angles, balanced geometrically. The point isn't grace and fluid movements, but to combine the speed of a spinning-top with an as sudden and precise a break in motion as that of a whirling dagger nailing the apple on top of the beautiful assistant's head, so vulnerably and trustingly stand does she. It is a war dance.
A great example of a Lezginka is usually given by the Chechen President, Ramzan Kadyrov:
I think what happened was that, as time went on, women started jumping into the fray. I would guess that this was a very, very late development because even today it is very conceivable for rivals over a woman to get into a fight if she dances with one of them and leaves the other alone. But, in any case, that the introduction of women into this dance is a new development is also evidenced by how thoroughly boring the woman's dance is compared to the man's: it is basically gliding in circles while making elegant gestures with the hands. The footwork, if any, is limited to imitation. Consider this video of Lezginka being performed by women at a Chechen Wedding, for example:
And that is the "evolutionary" curve that the Lezginka has gone through: it began as a war dance, women joined in, and it then became a spectacle for people to watch, vicariously enjoy, and clap for entertainment: the concert ends at 8 PM so you can get to work on time the next day. And that's generally the curve of culture from pre-modern to late modern. Savage and exhilarating in the beginning; beautiful-ish and civil toward the middle.
Here's a diagram of the steps so you can learn how to do a Lezginka :
Description of the moves :
Man: Raise your shoulders in a broad manner and keep your arms outstretched while bending them slightly in the same direction. Your fingers should be open, however, every so often, make a fist while bending your arms. Your legs should bend slightly while stomping on the ground and crossing your feet. The most important part of the Lesginka should be to be close to your female partner NEVER touching her. You should encircle her while moving your arms around her. You should give the impression of being jagged and hard, but also flowing at the same time.
Woman: Keep your arms raised above your shoulders while veiling your face with your fingers as if you were tickling the air. Walk softly, flutter close to your partner but also give him the impression that he needs to "follow" your lead. Maintain eye-contact with him while walking gently, crossing your feet. You ought to conjure a feeling of softness.