Lampito is a pretty one-dimensional character, and that one dimension is mostly an ethnic stereotype (ugh: the worst kind of stereotypes). Lampito shows up on the scene during Lysistrata's meaning of all the women of Greece. Lampito is there representing Sparta, Athens's mortal enemy.
Lampito is the model Spartan woman: she speaks a version of the Spartan dialect and is extremely muscular and athletic. Spartans were known for being ripped. There were also known for shouting "This is Sparta!" and generally being kick-butt.
The thing that gives Lampito a little bit more depth, though, is her eagerness to join in Lysistrata's plan. She does not yell "This is Sparta!" and go around stomping people with her sandaled feet… maybe because Lysistrata takes place in Athens. In any case, Lampito is just as eager to get the war over and done with as any of the Athenian housewives.
And she knows that sexytimes trumps war, at least historically:
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)
When it comes down to it, though, this willingness on Lampito's part may be less about adding depth to Lampito as a character than it is about showing that the Spartans aren't as dead-set on war as Aristophanes' Athenian audience might think.
Either way, Lampito plays a crucial role in the plot, even if she is onstage for only a brief time. When the Herald shows up from Sparta toward the play's end, he tells Cinesias that Lampito has lead all the women of Sparta on a sex-strike, making the Spartan men suffer bouts of painful erections. In this way, Lampito is behind the act that makes Cinesias convince the Athenians to make peace.
Lampito also has another pivotal role in Lysistrata: she brings up the subject of cash money. Sex strikes alone, in Lampito's understanding, ain't going to stop the war. Not only do you have to cut off the blood supply to the warriors' brains… you also have to cut off their moolah supply:
Lampito: "And we will convince our menfolk to keep a completely fair and honest peace. But how can anyone keep your Athenian rabble from acting like lunatics?"
Lysistrata: "Don't worry, we'll handle the persuasion on our side."
Lampito: "Not so, as long as your battleships are under canvas and your Goddess' temple has a bottomless fund of money."
Lysistrata: "No, that's also been well provided for: we're going to occupy the Acropolis this very day. The older women are assigned that part: while we're working out our agreement down here, they'll occupy the Acropolis, pretending to be up there for a sacrifice." (167-179)
Wow. Lampito is disciplined (she's buff), she's gutsy (for showing up in Athens in the first place), and she understands why it's important for everyone to do without money. Guess she really is Spartan.