A five-under-par 66 left the Australian fan favourite in a tie for fourth, three shots behind leading trio Shane Lowry, David Skinns and Austin Eckroat, heading into what shapes as a Sunday shootout.
Lee drained eight birdies, including five on the back nine, to find himself in the top five entering the final round of a PGA Tour event for only the second time.
"Yeah, very solid," Lee said.
"A couple bogeys where ... it happens.
"I made a lot of putts today and hit it really good. I'm very proud of the way I hung in there and finished."
The West Australian was equal second through 54 holes before finishing tied sixth at last year's Players Championship.
This week's field - featuring only one player from the world's top 20 - is considerably weaker, leaving Lee with a golden opportunity to crack his first win on the lucrative American tour.
The 25-year-old is already a two-time DP World Tour winner and is now one strong round from joining his world No.5 sister Minjee Lee as a US tour victor.Â
History, though, is against the Perth ace.
He shares fourth at 10 under with American Jacob Bridgeman (65), Scot Martin Laird (66), Taiwan's Kevin Yu (70) and Frenchman Victor Perez (70).
This is the 18th time the tournament - known as the Honda Classic until this year- has been contested at PGA National.
And it's proven to be hard to rally for a win there on Sunday: in the previous 17 tour events at PGA National, 11 eventual winners had at least a share of the lead after 54 holes and 16 were no worse than tied for second.
The exception is South Korea's Sungjae Im, who was fifth entering the final round in 2020.
The only players to rally from more than one stroke back entering the final round to win the Honda at PGA National were Sepp Straka (five back in 2022 when he prevailed over Lowry), Im (three back in 2020), Padraig Harrington (three back in 2015) and Russell Henley (two back in 2014).
"It can definitely go the wrong way," Lee said.
"It's a course where you could play really good and just shoot bad, and you can't really fake it around here.
"Hopefully you can hit some fairways and hit some good shots in and putt well."
Like Lee, Irishman Lowry and England's Skinns carded 66s, while American Eckroat had a 68 as they all moved to 13 under for the tournament.
Lowry is looking for his third victory on the PGA Tour, Skinns is trying for his first top-10 finish in 33 tour starts, while Eckroat is seeking a first tour win at his 50th attempt.
"Even though the scoring is pretty good this year, I like playing tough golf," said Lowry, the 2019 British Open champion who has shot in the 60s all three days.
"I like when everything is on the line a lot."
- with AP
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