There was only a difference of 0.5 points between one Lee and four Angelina Melnikova before the last branch.
Lee did not get the highest score in the standings but kept out and won with 0.135 points ahead of Brazilian Rebeca Andrade, who made some mistakes in her program.
Russian Angelina Melnikova took bronze.
It also finished Russian in fourth place through Vladislava Urazova who was 0.467 points behind the winner.
Lee was part of the American all-around team that took silver after Biles left the competition for a branch.
Biles cited mental illness as a reason to leave the competition and to the fact that she later struggled in the individual all-around.
This is the fifth Olympics in a row that an American wins the prestigious all-around event.