McCollum, who was ninth in the nation in scoring last season, made 10 of 16 field goal attempts and sank all nine of his free throw attempts.
Three other players scored in double figures for the Mountain Hawks (3-2), who have won three games in a row. Jordan Hamilton added 23 points, and Gabe Knutson and Mackey McKnight each scored 10. Lehigh shot 53.4 percent (31 of 58) from the field.
Lehigh went on an 11-0 run to grab a 25-7 lead with 11:56 to play in the first half. Liberty got as close as three points, at 58-55, with 11:58 remaining in the game.
John Caleb Sanders scored 18 points, David Minaya had 16 and Jesse Sanders had 12 for Liberty (2-3).