Last night, a coroner revealed that Cory had died from a heroin and alcohol overdose. His cause of death was determined following toxicology reports.
Lea's spokesperson has now released a statement, saying the devastated actress is grieving alongside Cory's equally distressed family.
Speaking to American magazine People, her rep said: "Lea is deeply grateful for all the love and support she's received from family, friends, and fans.
''Since Cory's passing, Lea has been grieving alongside his family and making appropriate arrangements with them."
The actress's rep described Cory's death as a "profound loss" and asked that the privacy of Lea and Cory's family is respected.
Cory, who starred as Finn Hudson in Glee, was found dead in his hotel room in Vancouver, Canada, on 13 July after failing to meet his scheduled check-out time.
Police ruled out foul play and, in a statement, the Coroners Service of British Columbia has since said: "At this point there is no evidence to suggest Mr. Monteith's death was anything other than a most sad and tragic accident."
Cory, 31, had been battling a drug and alcohol addiction but was looking well following a stint in rehab in April. At the time, Lea said she was "very proud" of him for facing up to his demons.
Since his passing, tributes have poured in for Cory, from both his Glee bosses and co-stars, along with fellow celebrities.
Memorabilia, candles and messages of condolences from fans have also been mounting up outside Paramount Studios in Hollywood, LA.
One star shaped trinket, decorated with musical notes, read: "Rock on Finn Hudson." Another simply said: "RIP Cory."
Watch the Coroners Service releasing their cause of death results: