The `Twilight` actor is said to have been romancing the 21-year-old actress for "almost four months" after meeting on the set of their forthcoming movie `Abduction`.
Since finishing the movie, Taylor is now working in Louisiana on `Twilight Saga: Breaking Dawn` and according to Us Weekly magazine, Lily "plans on hanging out there a lot."
The pair were first romantically linked in July, when it was reported the 18-year-old actor had seduced his co-star on the set of the film by "constantly flashing his shirtless six pack," despite her having a boyfriend.
A source said at the time: "Lily told pals that she wasn`t looking to fall in love, but soon realised she had strong romantic feelings.
"Taylor was smitten from day one, but Lily let him know she was in a relationship with a stuntman who was working on a Steven Spielberg movie in New Mexico. When the boyfriend got suspicious because Lily didn`t return calls promptly, he hopped a plane and turned up unannounced to confront her."