He will have a chance to make progress tomorrow on the easier Monterey Peninsula course with its larger greens and more generous fairways, before the final round back at the host course, Pebble Beach, where he hit his 63.
He believes he's a good chance to become the first Kiwi to win on the regular PGA Tour since Phil Tataurangi, who won the Invensys Classic at Las Vegas in 2002. Earlier that year Craig Perks won the Players Championship.
"Yep, I can win this tournament," Lee said confidently. "I am not too far away from the lead and, if I play well, anything can happen and I will give it my best to win. Everything will be alright."
He will have to do it against some of the biggest names in the game but Lee takes little notice of who is also in contention.
"I don't take any notice of what the media are saying or look at leaderboards. I have really good people around me who help me get ready to play.
"I am going to keep doing what I have been doing the past couple of days and see what happens. What the other players shoot is out of my control but I will be giving it my best. It is really hard to win any professional golf tournament so you need to take your chances."
He thinks the Monterey Peninsula course will suit him in the same way Pebble Beach did on day one.
"It seems like the same sort of course as Pebble Beach, actually, so I will go and try to play like I did there. I know that I need to keep attacking and making birdies. I feel comfortable out here. When I am in contention I normally play well because I like to play attacking golf."
Lee, who in 2010 became the youngest amateur to win on the European Tour when he claimed the Johnnie Walker Championship, said his game has developed a lot since the time he was the game's top-ranked amateur.
"I feel like I have come a long way. I am more experienced than I was a couple of years ago and that helps in the hard situations. I have improved my scoring because I make more pars or birdies from positions that I would not have before. I keep fighting and with experience I know how to score better.
"I just need to stay patient. I am really young. I am only 21 years old and I am happy with the progress that I have made in my professional career so far. I am happy to be on the PGA Tour it is a dream come true for me. It is the tour that I always wanted to play on so it is great to be doing it every week. I am playing with the best golfers in the world and it is fun to be competing with them."