"I've always kind of lived in their shadows, and now is the first time in my life when I get to own my life and stand on my own. I love being my mother's daughter, and it's something I always will be, but now I get to be just Billie," Lourd told the magazine.
"It is [scary]," she confessed. "It's a lot of pressure, because she had such an incredible legacy, and now I have to uphold that and make it evolve in my own way."
Reynolds, who starred in such films as Singin' in the Rain, died of a stroke Dec. 28, one day after Fisher, who played Princess Leia in the Star Wars movies, died following a heart attack. Lourd said remembering her mom's sense of humor helped her cope with the losses.
"Oh, [humor is] so important," the star said. "If life's not funny, then it's just true -- and that would be unacceptable."
"Even when she died, that was what got me through that whole thing," she shared. "When Debbie died the next day, I could just picture her saying, 'Well, she's upstaging me once again, of course -- she had to.'"
Lourd paid tribute to Fisher at a Star Wars celebration in April, saying her mom taught her "by her own example." She will appear with the late actress in Star Wars: The Last Jedi, and will also star in American Horror Story: Cult.