Lee made the turn in one under par 34 and eventually reached three under, but made three consecutive bogeys to drop back to even par and on the cusp of the cut-line.
The former US Amateur champion needs a strong run of form to secure his place in the top 125 on the standings and qualify for the first Fed Ex Cup playoff event in late August.
Meanwhile, on the web.com tour, Tim Wilkinson was one over through 11 holes at the Children's Hospital Invitational in Ohio before play was suspended due to inclement weather.
The left-handed professional from Manawatu, who is currently the leading Kiwi in 46th place on the web.com order of merit, is in a share of 76th place at the OSU Golf Club.
Hamilton professional Steve Alker, who finished tied 19th at the British Open last week, carded a three over par 74 to be in a share of 129th place.
The 40-year-old Kiwi, who is currently 67th on the order of merit, is attempting to climb inside the top 25 to automatically qualify for the PGA Tour in 2013.