Spieth leads at eight-under by a stroke over the Swede, who shot a two-over 72 to slide back into second after a dominant first two rounds. Rickie Fowler and Paul Casey are three strokes further back, and Rory McIlroy shares fifth place with Zach Johnson.
Lee has made 10 of his last 11 cuts, and another strong finish would cap off a brilliant PGA Tour season, as well as leading nicely into his debut foray into the President's Cup.
Meanwhile, fellow Kiwis Tim Wilkinson and Steven Alker will be looking to join Lee on the PGA Tour again next season.
Alker sits in a tie for 15th through three rounds of the Nationwide Children's Hospital Championship on the Web.com Tour Playoffs, while Wilkinson is in a share of 12th.
The top 25 players in the playoffs get their PGA Tour cards, and with one tournament remaining Alker sits in 34th, and Wilkinson in 22nd.