  Around $10^5$ strongly lensed galaxies are expected to be discovered with
Euclid and the LSST. Utilising these large samples to study the inner structure
of lens galaxies requires source redshifts, to turn lens models into mass
measurements. However, obtaining spectroscopic source redshifts for large lens
samples is prohibitive with the capacity of spectroscopic facilities.
Alternatively, we study the possibility of obtaining source photometric
redshifts (photo-zs) for large lens samples. Our strategy consists of
deblending the source and lens light by simultaneously modelling the lens and
background source in all available photometric bands, and feeding the derived
source colours to a template-fitting photo-z algorithm. We describe the lens
and source light with a Sersic profile, and the lens mass with a Singular
Isothermal Ellipsoid. We test our approach on a simulated and a real sample of
lenses, both in broad-band photometry of the Hyper Suprime-Cam survey. We
identify the deviations of the lens light from a Sersic profile and the
contrast between the lens and source image as the main drivers of the source
colour measurement error. We split the real sample based on the ratio $\Lambda$
of the lens to source surface brightness measured at the image locations. In
the $\Lambda<1$ regime, the photo-z outlier fraction is $20\%$, and the
accuracy of photo-z estimation is limited by the performance of
template-fitting process. In the opposite regime, the photo-z outlier fraction
is $75\%$, and the errors from the source colour measurements dominate the
photo-z uncertainty. Measuring source photo-zs for lenses with $\Lambda<1$
poses no particular challenges, compared to isolated galaxies. For systems with
significant lens light contamination, however, improving the description of the
surface brightness distribution of the lens is required: a single Sersic model
is not sufficiently accurate.
