Although the pair hadn't been photographed together in recent days, a source close to the actress, 26, tells PEOPLE, "They were happy and very in love."
Michele has not spoken publicly yet about her boyfriend's death, but her rep told PEOPLE in a statement on Sunday: "We ask that everyone kindly respect Lea's privacy during this devastating time."
During the course of their relationship of more than a year, Michele gushed to PEOPLE about her Glee costar, 31.
"I love working with Cory, I always have," she said late last year. "He really, really inspires me, and he motivates me and I think he's just so talented. Working with him has been one of the best experiences of this whole process."
The actress notably stood by her man's side when he voluntarily entered a month-long treatment program in April for substance addiction.
The following month, the pair were photographed vacationing together in Puerto Vallarta, Mexico.
Fans of Monteith's may make donations in his name to three charities that were especially important to him: Project Limelight Society, which exposes youth living in Vancouver's Downtown Eastside to the arts; Virgin Unite, founded to support entrepreneurial efforts to better the world; and Chrysalis, which helps homeless and low-income individuals find employment.
Reporting by AILI NAHAS