The escape velocity formula has nothing to do with what is trying to escape. That means that the mass of the lunar module is not needed.
Formula
v = sqrt( (2 * G * M) / R)
Givens
v = ??
G = 6.67 * 10^-11 This is the gravitational constant.
M = 7.34 * 10^22 kg
R = 1.74 * 10^6 m
Solution
v = sqrt( 2 * 6.67 * 10^- 11 * 7.34*10^22/1.74*10^6)
v = sqrt(9.79156* 10^12 / 1.74 * 10^6)
v = sqrt(5.627 * 10^6)
v = 2372 m/s