It is essential to understand the pump-induced lensing and aberration effects in solid-state lasers, such as Alexandrite, since these set limits on laser power scaling whilst maintaining high spatial TEM00 beam quality. In this work, we present direct wavefront measurements of pump-induced lensing and spherical aberration using a Shack-Hartmann wavefront sensor, for the first time, in a diode-pumped Alexandrite laser, and under both non-lasing and lasing conditions. The lens dioptric power is found to be weakly sub-linear with respect to the absorbed pump power, and under lasing, the lensing power is observed to decrease to 60 % of its non-lasing value. The results are inconsistent with a thermal lens model but a fuller theoretical formulation is made of a combined thermal and population lens model giving good quantitative agreement to the observed pump power dependence of the induced-lensing under non-lasing conditions and the reduced lensing under lasing conditions. The deduced value for the difference in excited to ground state polarizability is consistent with prior measurement estimates for other chromium-doped gain media. The finding of this paper provide new insight into pump-induced lensing in Alexandrite and also provides a basis for a fast saturable population lens mechanism to account for self-Q-switching observed recently in Alexandrite laser systems.