Woodland, who has fought back from brain surgery in 2023, will take a one-shot lead into the final round after posting a five-under 65 and reach 18 under at Memorial Park on Saturday.
Denmark's Nicolai Højgaard charged with a 63 to be second and the only player within five shots of 2019 US Open champion Woodland.
World No.31 Lee birdied two of the last three holes as he carded a 67 to head that chasing pack, tied third at 12 under with American Michael Thorbjornsen (66).
Fellow Australian Jason Day had a 68 to be a further shot back while Adam Scott (68) was tied 10th at nine under with Karl Vilips (71) at six under.
Woodland has become a popular figure in golf for the way he has handled his recovery from his brain surgery and earlier this month opening up on his struggles with post-traumatic syndrome disorder.
His golf has looked as good as ever.
"I've just got to take a deep breath," Woodland said. "Tomorrow just don't get ahead of yourself. I'm here, I put myself in this position for a reason, so take a deep breath and maintain what I'm doing."
Nearest challenger Højgaard is running hot, having made 15 birdies and one eagle the last two rounds.
The 25-year-old has three wins on the European tour, including the DP World Tour Championship at the end of 2023 but has yet to win on the PGA Tour.
Sunday will be also big for Thorbjornsen, who is No. 6 in the world. The top 50 after this week earn Masters invitations, and he likely needs no better than eighth place.
Lee, Day, Scott and fellow Aussie Cameron Smith are already in the Masters field.
Højgaard is still not in the Masters, though at No.47 he is virtually a lock to stay in the top 50.
Woodland would need nothing short of a victory to get back to the Masters, even a perk such as that is secondary considering all he has gone through.
The surgery was to remove a big part of a lesion that was producing unfounded fears of dying.
He returned to the PGA Tour at the start of 2024, but only recently did he share struggles with PTSD, how he would begin crying in the middle of the round and sometimes hide in the bathroom.
To share that publicly was an enormous relief for Woodland, who said earlier this week he felt "1,000 pounds lighter."
22°C