Narrator? What narrator? Lysistrata is a play and it doesn't have a narrator at all. Instead of hearing what characters do, we actually see them do it.
We don't get a God's-eye view of what the characters are thinking, but we do get a bird's-eye view of everything they're doing and saying. And that, folks, is the definition of Third Person Objective. We see it all: all the meetings, the arguments, and the erections. Once you see Lysistrara from your Third Person Objective seat, you will not be able to unsee Lysistrata.