Starting on the back nine, Gee eagled the par-4 14th hole but bogeyed the 18th before carding three birdies on the front nine.
Lundberg hit six birdies and lost a stroke on the par-3 second. The Swede, who came through the European Tour Qualifying School for a third straight year, is looking for his first title since winning the Russian Open for a second time in 2008.
Lundberg said he's improved since working with new coach Neil Jordan: "I am more solid from the tee onto the green. You have to be careful out there, and don't take unnecessary chances."
Defending champion Joost Luiten from the Netherlands hit three birdies in his opening four holes. Later, however, he struggled to hit the fairways and dropped to 1 over before finishing his round level par with his fourth birdie on the 17th.
Miguel Angel Jimenez overcame three bogeys in the first eight holes to card a 2-under 70.
The 50-year-old Spaniard, who resides in Vienna since marrying an Austrian in May, is seeking his third win of the season. Starting on the back nine, he bogeyed the par-4 11th and 17th and the par-3 14th but recovered with four birdies.
"It's OK, it's under par," Jimenez said. "It's not easy because of the wind."