  The elliptical power-law (EPL) model of the mass in a galaxy is widely used
in strong gravitational lensing analyses. However, the distribution of mass in
real galaxies is more complex. We quantify the biases due to this model
mismatch by simulating and then analysing mock {\it Hubble Space Telescope}
imaging of lenses with mass distributions inferred from SDSS-MaNGA stellar
dynamics data. We find accurate recovery of source galaxy morphology, except
for a slight tendency to infer sources to be more compact than their true size.
The Einstein radius of the lens is also robustly recovered with 0.1% accuracy,
as is the global density slope, with 2.5% relative systematic error, compared
to the 3.4% intrinsic dispersion. However, asymmetry in real lenses also leads
to a spurious fitted `external shear' with typical strength, $\gamma_{\rm
ext}=0.015$. Furthermore, time delays inferred from lens modelling without
measurements of stellar dynamics are typically underestimated by $\sim$5%.
Using such measurements from a sub-sample of 37 lenses would bias measurements
of the Hubble constant $H_0$ by $\sim$9%. Although this work is based on a
particular set of MaNGA galaxies, and the specific value of the detected biases
may change for another set of strong lenses, our results strongly suggest the
next generation cosmography needs to use more complex lens mass models.
