The 'Not Fair' singer - who has been single since January - propositioned the frontman after her performance at the Oxegen music festival in Ireland over the weekend.
She told MTV News: "If I had to share a tent with anyone it would be Gary Lightbody. His band look like they would be clean - I don't know if I would say the same for myself!
"I have just bought a yurt, which I prefer to a normal tent, so there would be plenty of room for him and the band to join me."
A yurt is a felt-covered, wood lattice-framed portable sleeping structure traditionally used by nomads in Central Asia.
It seems Gary is equally as smitten with Lily.
When Snow Patrol took to the stage at the festival in Punchestown Racecourse, County Kildare, Gary dedicated the band's song 'Shut Your Eyes' to the 24-year-old brunette.
Gary, 33, said: "I am going to sing this song for Lily Allen. She is a great girl, she is really something. So this one is dedicated to her."
Lily recently revealed she falls hard for new boyfriends.
She said: "I fall in love easily. It's a big problem for me. I just can't help it, I love flirting, kissing, the whole first date stuff. I'm an all or nothing girl and it gets me into trouble.
"Do I get easily heartbroken? Yes, always, because I throw myself right in. I'm very, very emotional."