  Many new strong gravitational lensing (SGL) systems have been discovered in
the last two decades with the advent of powerful new space and ground-based
telescopes. The effect of the lens mass model (usually the power-law mass
model) on cosmological parameters constraints has been performed recently in
literature. In this paper, by using SGL systems and Supernovae type Ia
observations, we explore if the power-law mass density profile is consistent
with the cosmic distance duality relation (CDDR),
$D_L(1+z)^{-2}/D_A=\eta(z)=1$, by considering different lens mass intervals. It
has been obtained that the verification of the CDDR validity is significantly
dependent on lens mass interval considered: the sub-sample with $\sigma_{ap}
\geq 300$ km/s (where $\sigma_{ap}$ is the lens apparent stellar velocity
dispersion) is in full agreement with the CDDR validity, the sub-sample with
intermediate $\sigma_{ap}$ values ($200 \leq \sigma_{ap} < 300)$ km/s is
marginally consistent with $\eta=1$ and, finally, the sub-sample with low
$\sigma_{ap}$ values ($\sigma_{ap} < 200$ km/s) ruled out the CDDR validity
with high statistical confidence.
