"He gave me the gift of family," the Grammy-winning singer said. "I will forever be grateful."
The two-time Grammy winner returned to social media this week for the first time since 21-year-old Beckett's death. She also hinted that new music is on the way.
"We struggled with what else we could have done to save him," the "Come To My Window" singer wrote on Instagram.
She didn't name their paramour in common, telling the "Once Upon a Time in Hollywood" star they'd "talk about that later."
She has been open about using cannabis to manage pain from cancer.
"God, hopefully things will be different in another year," the singer told HuffPost.
It "breaks my heart a little bit."