These two plays are alike in that strong women speak up in an attempt to control the outcomes of unpleasant situations. In Antigone's case, she is unhappy with the decree that her loved one will not be given an acceptable burial. Against the law, she buries him and faces death and the title of "traitor".
The women in Lysistrata are unhappy that their men are wrapped up in a war that seems to never end. Therefore, they get together (the women from both sides of the fray) and decide to withhold sexual pleasure from their men until the men declare an end to the fighting.
Both plays are written in a time when women were not given many rights and were expected to be "arm candy" only--lovely to look upon, silent, and obedient. It is unusual that these women would all take such strong stands in the man's world which they live.
They are unalike in the way that they flex their womanly muscles. Antigone never hinted at sex as a way to solve the problem she faced--it was more logic and character appeals that she uses to convince Creon to change his mind.