"Our geographical designation has been usurped by certain ladies who have no connection whatsoever with Lesbos," he said.
"I don't see how the word can be an insult," Evangelia Vlami said.
"We don't think doubt can be cast on dictionaries ... even the United Nations refer to us as lesbians."
Also called Mytilene, after its capital, Lesbos is famed as the birthplace of Sappho. The island, particularly the lyric poet's reputed home town of Eressos, is a favoured holiday destination for gay women.
"This is not an aggressive act against gay women," Lambrou said.
"Can't a woman just say: I am from the island of Lesbos?""
Evangelia Vlami, Homosexual and Lesbian Community of Greece
"Let them visit Lesbos and get married and whatever they like. We just want [the group] to remove the word lesbian from their title."
He said that the plaintiffs targeted the group because it is the only officially registered gay group in Greece to use the word lesbian in its name.
The case will be heard in an Athens court on June 10.
Sappho lived from the late 7th to the early 6th century BC and is considered one of the greatest poets of antiquity.
Many of her poems contain passionate references to love for other women.
Lambrou said the word "lesbian" has only been linked with gay women in the past few decades.
"But we have been Lesbians for thousands of years," said Lambrou, who publishes a small magazine on ancient Greek religion and technology that frequently criticises the Christian Church.
Vlami, the gay group spokeswoman, said any misunderstanding can easily be resolved through linguistics.
"Most people from Lesbos prefer to use the word Mytilene, which is the more ancient version and because some people may be afraid of being misunderstood," she said.
"I don't see what the problem is ... Can't a woman just say: I am from the island of Lesbos?"
Lambrou says Sappho was not gay.
"But even if we assume she was, how can 250,000 people of Lesbian descent - including women - be considered homosexual?"