  Strong gravitational lens system catalogues are typically used to constrain a
combination of cosmological and empirical lens mass model parameters, even
though the simplest singular isothermal sphere (SIS) models yield a $\chi^2$
per degree of freedom $\simeq 2$. To date, this problem has been alleviated by
introducing additional empirical parameters in the extended power law (EPL)
models and constraints from high resolution imagery. The EPL parameters are
taken to vary from lens to lens, rather than defining universal lens profiles.
We investigate these lens models using Bayesian methods through a novel
alternative that treats spatial curvature via the non-FLRW Timescape cosmology.
We apply Markov Chain Monte Carlo methods using the catalogue of 161 lens
systems of Chen et al (arXiv:1809.09845) to simulate large mock catalogues for:
(i) the standard $\Lambda$CDM model with zero spatial curvature; and (ii) the
Timescape model. Furthermore, this methodology can be applied to any
cosmological model. In agreement with previous results we find that in
combination with SIS parameters, models with zero FLRW spatial curvature fit
better as the free parameter approaches an unphysical empty universe,
$\Omega_{\rm M0}\to0$. By contrast, the Timescape cosmology is found to prefer
parameter values in which its cosmological parameter, the present void
fraction, is driven to $f_{\rm v0}\to0.73$ matches, close to values found to
best fit independent cosmological data sets: supernovae Ia distances and cosmic
microwave background. This conclusion holds for a large range of seed values
$f_{\rm v0}\to0.73\in\{0.1,0.9\}$, and for Timescape fits to both Timescape and
FLRW mocks. Regardless of cosmology, unphysical estimates of the distance
ratios given from power-law lens models result in poor goodness of fit.
Nonetheless, the results are consistent with non-FLRW spatial curvature
evolution.
