The spokesperson told People: "We ask that everyone kindly respect Lea's privacy during this devastating time."
The 31-year-old actor was found dead in Vancouver's Fairmont Pacific Rim Hotel yesterday (July 13). Police are yet to confirm the cause of death, but an autopsy will take place on Monday.
Cory spent time in rehab for substance addiction earlier this year, and had the full support of actress Lea, 26.
"I love and support Cory and will stand by him through this," she said.
In a recent interview, Lea said of her boyfriend of two years: "I don't even remember a time when he wasn't my boyfriend. No one knows me better than Cory.
"He makes me feel like I can do anything. For the first time in my life, I feel really, really settled and happy. I feel like the luckiest girl in the world."
Cory is said to have spent his last hours enjoying an evening out with friends before he tragically passed away alone in the hotel room.
He was found by cleaning staff when he didn't check out of his hotel room. Paramedics were called who declared him dead at the scene shortly after noon. Police said there were no signs of foul play.