One of the names J.R.R.Tolkien used for England in his early writings (BoLT2).
In one of the versions of Eriol's story, Eriol - the mortal, reaches the isle of the Elves - TolEressŽa, and the Elves who dwelled there called him Luthien - the man from Luthany = "friend" and "friendship" respectively.
In that version of the story, Luthany (=England) were once the westernmost lands where Ingwe was king and where the Elves sought refuge from Men after disastrous wars (see Faring Forth and Of the Seven Invasions). From there the defeated Elves returned to TolEressŽa. In Luthany, however, Elves and Men lived for some time in friendly relations and from this comes the name itself, Luthany meaning friendship. But then Luthany was invaded by evil Men (see Of the Seven Invasions), some of whom did not even believe in the existance of the Elves ( the Rumhoth = the Romans), and so the fairies had to leave those lands and set sail to TolEressŽa. There they settled and gave to their new towns and places names of old times, when still living in Luthany (Kortirion, Tavrobel etc.)and they spoke the language once spoken in Luthany by both - Elves and friendly Men (thus Eriol, when he reached TolEressŽa, found out that he could understand the language spoken by the Elves who dwelled there).
The king of Luthany Ingwe (him being once an Elf but in other versions - a mortal man, who drank limpe and thus became immortal and also believed to be Eriol's father) searched for TolEressŽa but was lost (in some other versions he reached the Lost Island and built Kortirion).
After his departure, Luthany was separated from the Great Lands by a channel and so became an island.
Luthany as a name used by Tolkien for England was sometimes changed for Luthien as well.