Lee, who is hovering around the top 50 on the FedEx Cup standings, was the best of the Kiwis in Texas, although Steven Alker delivered a one-under 69 during his first round, which included four birdies and three bogeys, to sit in a tie for 33rd.
Alker came into the tournament in 181st on the FedEx Cup standings and making another cut this week will help boost his status on tour.
Manawatu's Tim Wilkinson struggled in his first round as he fired a two-over 72 to sit in a share of 108th. Wilkinson is 178th on the FedEx Cup pecking order and could also do with a decent showing this week.
Meanwhile, North Shore professional Michael Hendry made a blistering start to the Mizuno Open in Japan with a nine-under 63 to hold a two-stroke lead after the opening round at the JFE Setonaikai Golf Club.
Hendry, who recorded his maiden win on the Japan Tour earlier this year, will be chasing a handful of spots for The Open Championship in Scotland in July that are up for grabs at this week's tournament.
On the PGA Tour China circuit, Josh Geary, who leads the order of merit, carded a five-under 67 at the Lanhai Open's first round yesterday, to have a share of the lead.