This is an interesting question. A good way to answer this question is by offering a brief summary of the comedy by Aristophanes. In this comedy, the women ban together and make a pact that they would withhold sexual relations from their husband until the long Peloponnesian war is put to an end. The women take matters into their own hand, as the war lingers for several decades.
A modern audience may have a hard time appreciating the comedy, Lysistrata, for several reasons. First, there is different social context. To appreciate fully the logic of the comedy, we need to be in a protracted war where both sides have experienced great loss.
Second, we need to live in a society, where there is a greater social divide between men and women. In other words, the very fact that the protagonist Lysistrata and other women orchestrated this ban on sexual relations is radical from a historical point of view. It is a social order that has been inverted.
Finally, the comedy would have to be brought up to date, that is, made contemporary, for most people to connect with such an old work.