Plomb has scored in double figures in every game this season and 23 straight games overall.
Kevin Ferguson scored 15 points, Adam Roe added a career-high 11, and Larry Toomey grabbed a career-high 11 rebounds for the Black Knights (10-3, 1-0), who made 12 of 26 3-pointers (46 percent).
Army led 45-34 at halftime, but Lehigh closed within 47-41 on a 3-pointer by Austin Price.
Plomb hit his second 3-pointer for a nine-point Army lead with 1:34 left, but Price hit back-to-back 3s with 3 seconds to go to pull Lehigh within five before time ran out.
Tim Kempton scored a career-high 28 points, Price had 22, Jesse Chuku added 17 with five 3s, and Kahron Ross grabbed a career-high 12 rebounds for the Mountain Hawks (2-10, 0-1).