The new couple - who also play on-screen lovers Finn Hudson and Rachel Berry in musical drama 'Glee' - have been spotted enjoying a cosy sushi dinner date in the 29-year-old actor's home city of Vancouver.
An eyewitness said: ''They came in Saturday (25.02.12) night for dinner. Cory is well known here because he comes in all the time. They sat at a table at The Front of the restaurant in the corner. They wore hats and both ordered Ichi rolls.''
The pair - who were also seen having a romantic meal in Los Angeles on Valentine's Day (14.02.12) - managed to keep a low profile before leaving a generous tip.
The source told Life & Style magazine: ''A woman recognised the pair and though they politely said that they were trying to lay low, they were still very nice to her. No one else bothered them.''
Lea, 25, split from Broadway star Theo Stockman after 17 months of dating in September 2011, and admitted last year that if she was going to get romantically involved with any other cast members then it would be Cory.
She explained: ''For me, if it was going to happen with anybody, it would have happened with Cory.
''As long as I get to have scenes with Cory, it makes me really happy.''