The 21-year-old American, who won all-around gold in Tokyo three years ago after Biles's sudden withdrawal due to mental health struggles, was diagnosed with two undisclosed kidney conditions in early 2023.
"I mean, literally, six months ago I didn't even consider I would be here competing today. That was an achievement in itself," said Lee.
The gymnast from Minnesota's road back to the pinnacle of her sport has been as challenging as that of Biles.
She had been bidding to become the first woman since Czech Vera Caslavska in 1968 to win consecutive all-around titles.
But in an unprecedented clash between Olympic champions the fact that it was 2016 all-around gold medallist Biles who prevailed did not matter to Lee.
"I'm so happy right now. I feel like everything that I've done has paid off," said Lee.
"Honestly, I wasn't expecting to be on the podium. To just be here has been absolutely amazing.
"I definitely got a little emotional after my floor routine. Just seeing the score come up was just insane."
Lee had been down in seventh after the opening of four apparatus -- the vault.
She clawed her way back to fifth on the uneven bars, was joint fourth after balance beam and sealed a medal with her elegant floor routine that brought the crowd to their feet in Bercy Arena.
"In that moment, I was just kind of like laughing. I mean, I was super happy, but I was in shock too," she told journalists.
"Because, like I said, I didn't think I would make the podium. Going into that floor routine tonight I told myself to just really have fun and let my gymnastics do its thing."
A year ago she was unable to get out of bed with her health problems and this week Lee also took team gold with the United States to bring her tally to five Olympic medals, two of them gold.
She will also compete in the finals on the uneven bars and balance beam at the weekend.
"It's (been) a lot of mental work, because it's been hard for me to continue," she explained.
"Right now I'm just proud to be where I'm at and doing the things that I'm doing, because nobody really believed in me. It's about not giving up."
