Lamb had scoring throws of 29, 9, and 30 yards to three different receivers. He was 18 of 24 for 291 yards passing to lead the Mountaineers (4-1, 1-0 Sun Belt Conference) to their third-straight win.
Zach Matics kicked field goals of 22 and 39 yards, and Appalachian State led 30-3 late in the third quarter.
Marcus Cox ran for 76 yards on 19 carries in three quarters, snapping his seven-game streak of 100 yards or more rushing for the Mountaineers, two games shy of the school record set by John Settle in 1986.
Latrell Gibbs returned an interception 53 yards for a touchdown midway through the fourth quarter, his second pick-6 and fifth interception of the season.
Wil Lutz kicked a 25-yard field goal for Georgia State (1-4, 1-1).