Injunction sought
In court papers, the plaintiffs allege that the Greek government is so embarrassed by the term Lesbian that it has been forced to rename the island after its capital, Mytilini.
map of Lesbos
An early court date has now been set for judges to decide whether to grant an injunction against the Homosexual and Lesbian Community of Greece and to order it to change its name.
A spokeswoman for the group has described the case as a groundless violation of freedom of expression, and has pledged to fight it.
The term lesbian originated from the poet Sappho, who was a native of Lesbos.
Sappho expressed her love of other women in poetry written during the 7th Century BC.
But according to Mr Lambrou, new historical research has discovered that Sappho had a family, and committed suicide for the love of a man.