Lappin began attending Boston University in the fall of 1987, shortly after being drafted by his home-town Chicago Blackhawks. He played two good but unspectacular years for the Terriers, taking some time off during his sophomore season to play for Team USA at the World Junior Championships. After the season, Lappin decided to leave BU and transfer. Due to NCAA rules, because he was heading to another Division I program he would have to sit out a season. Fortunately, Lappin was still eligible to play junior hockey and was able to play for the Brockville Braves in 1990. He turned in a remarkable performance, scoring nearly three points per game and was named the league MVP.