Euclid is expected to discover approximately 170,000 strong gravitational lenses over its nominal survey, increasing the number of known systems by roughly two orders of magnitude. This unprecedented sample will enable not only statistical studies of the overall lens population, but also detailed investigations subclasses, such as double-source-plane lenses and edge-on spiral galaxies, which provide powerful constraints on the distribution of dark matter. For edge-on lenses, we model the baryonic component (informed by the light) separately from the dark matter halo, allowing the two mass distributions to be constrained independently. First results indicate a dark matter density profile that is shallower than the canonical NFW profile (with an uncertainty of ~10-25% per object from photometric data only), with a halo that is close to round in projection. Models that omit a dark matter halo require unphysically high bulge mass-to-light ratios, reinforcing the standard dark matter interpretation over alternatives such as MOND.