The 27-year-old said Nigerian the victory reflected Atalanta's rising confidence. "It's a big performance for the team. It's a good victory away from home," Lookman said.
"We knew we had to create chances again in the second half, and it's pretty good that we scored three goals quickly. The team are gradually gaining that confidence."
Frankfurt started brightly. Fares Chaibi forced Marco Carnesecchi into a superb early save, and Robin Koch headed wide soon after.
Atalanta grew into the game, with Lookman striking the post before half-time and Gianluca Scamacca hitting the same upright seconds later.
Atalanta struck on 60 minutes when Charles De Ketelaere floated a fine cross for Lookman, who volleyed inside the left post.
Two minutes later, Lookman burst forward and threaded a precise pass for Ederson to finish under Michael Zetterer.
Frankfurt unraveled. Scamacca hit the bar with a fierce effort, and De Ketelaere reacted quickest to sweep in the rebound for the third. Zetterer then denied Berat Djimsiti, but Atalanta were already cruising.
Atalanta remain just outside the top-eight qualification places and know they must maintain this level when hosting world champions Chelsea on matchday six.
Frankfurt, with only one win from five group matches and back-to-back heavy home defeats, now face a difficult fight to stay in the competition.