Fraser's round included seven birdies, five on the front nine, but back-to-back bogeys at the 11th and 12th holes kept him from grabbing the outright overnight advantage.
Lundberg's lone bogey at the Belfry's Brabazon golf course came at the par-3 14th hole, giving him six birdies in his best 18 holes this season.
Five players, one defending champion Lee Westwood, share third place at 4-under 68 and seven players are tied for eighth place at 3-under 69.
Last year, Westwood won this tournament by five strokes.
"I was in a good frame of mind out there," Westwood told the BBC about his third place standing. "I enjoy playing here and it suits my game and this week means a lot to me."
Swim Week Miami Beach 2014 [PHOTOS]