She said the album was '80s-inspired and was made for "anyone who has ever been in love (or) hate".
"Ella & Jack worked on most of this album in our apartment and it was a privilege to watch her create and feed her little snacks," said Dunham.
"For anyone who has ever been in love, been in hate, felt like they were living in the dizzying lights of an 80s movie- Melodrama is your album and Green Light is your jam," she wrote.
Lorde's bestie Taylor Swift also celebrated the release of Green Light, calling it "a magnificent bop for the ages".
Lorde hasn't revealed a release date for her new album, but she has festival performances booked at Coachella in April and the Governor's Ball in June.