"I called her and said, 'I don't know where I'm going to go because my house is swarmed (with reporters)," the 27-year-old told the December issue of Elle. "She was like, 'Oh, you're going to stay at my house.' Like it was nothing."
Mum-of-two Kate, who became close to Lea when she joined the cast of Glee in 2012 as dance teacher Cassandra July, also opened her home up to Lea’s loved ones.
"She let my family stay there, and any of my friends. She made sure that in the refrigerator were my favourite juices," Lea said.
"I'll never be able to thank her, truly, for what she did for me."
To the shock of his friends, family and fans, Cory died in July at the age of 31 from a mixed drug toxicity. He was memorialised in an episode of Glee titled The Quarterback, which dealt with the death of his character Finn Hudson.
Cory's passing is something Lea continues to deal with every day.
"Now that I'm in this position, you can choose to rise, which is what I'm going to try to do," she said.
"It's very hard and you have to be very strong to come out of this alive, but I think by doing the best for myself, by showing that you don’t have to lose yourself, maybe someone else will feel some sort of strength or comfort."
"I know that Cory would want nothing more than for me to take this situation and use it to help people," she added. "I don't know if I will. I don't know how."