Lappe was the team's top scorer both the 2009–10 season (17 goals) and the 2010–11 season (13 goals), as they finished in second place behind FC Ismaning – enough to earn promotion to the Regionalliga Süd, as Ismaning denied the opportunity to go up. Ingolstadt II finished in seventh place in the 2011–12 season, with Lappe scoring 18 goals - more than anyone else in the division. This earned him a call-up to the first-team - he made four appearances in the 2. Bundesliga, his debut as a substitute for Ahmed Akaïchi in a 2–0 defeat against TSV 1860 München in November 2011.
Lappe was not involved in the Ingolstadt first team at the beginning of the 2012–13 season, but scored prolifically for the reserves, now in the Regionalliga Bayern, following a restructuring of the league. 21 goals before the winter-break saw him brought back in the first-team fold, and he made an immediate impact, scoring the opening goal in a 2–0 win over FSV Frankfurt, his first 2. Bundesliga goal.