lord of the rings - When were Beren and Luthien alive?

Luthien was born in Doriath in the years of the Trees before the Sun first rose. Beren lived about 400 years after the Sun first rose in the First Age, which would have been about 6000 years before the events of The Lord of the Rings.

They both died, and were allowed to return to Middle-Earth by Mandos. But then Luthien, who was an elf, was made into a mortal, and they both died permanently late in the First Age.