There's no room for darkness in Lysistrata. This is pure, filthy comedy through and through. Even though it deals with weighty subject matter like war, it's only touches upon Real Talk subjects through the lens of a much lighter subject—sex. Lots and lots of sex.
Or rather, lots and lots of talk about sex, since this is about a sex strike, after all. Practically every line in this play contains some sort of sexual double meaning, and there are all kinds of other highjinks as well. These make the play light and fun. The only tears this baby is going to provoke will be from laughter.
Even if you start to wrinkle your brow at the thought of all those brave Greek men dying, an exchange like this will clear the storm clouds away:
Calonice: "Well, what if we did abstain from, uh, what you say, which heaven forbid: would peace be likelier to come on that account?" Lysistrata: "Absolutely, by the Two Goddesses. If we sat around at home all made up, and walked past them wearing only our diaphanous underwear, with our pubes all plucked in a neat triangle, and our husbands got hard and hankered to ball us, but we didn't go near them and kept away, they'd sue for peace, and pretty quick, you can count on that!" Lampito: "Like Menelaus! As soon as he peeked at bare Helen's melons, he threw his sword away, I reckon." (146-156)
Even the women in this play are more interested in making bawdy wisecracks than dwelling on the fact that men are dying. And honestly, the men in this play seem to think that dying is a better alternative to never getting laid again. This keeps it nice and light (though not family-friendly).