We present gravitational lens models for 20 strong gravitational lens systems observed as part of the Sloan WFC Edge-on Late-type Lens Survey (SWELLS) project. 15 of the lenses are taken from Paper I, while five are newly discovered systems. The systems are galaxy–galaxy lenses where the foreground deflector has an inclined disc, with a wide range of morphological types, from late-type spiral to lenticular. For each system, we compare the total mass inside the critical curve inferred from gravitational lens modelling to the stellar mass inferred from stellar population synthesis (SPS) models, computing the stellar mass fraction f*≡MSPS/Mlens. We find that, for the lower mass SWELLS systems, adoption of a Salpeter stellar initial mass function (IMF) leads to estimates of f* that exceed 1. This is unphysical and provides strong evidence against the Salpeter IMF being valid for these systems. Taking the lower mass end of the SWELLS sample (σSIE < 230 km s−1), we find that the IMF is lighter (in terms of stellar mass-to-light ratio) than Salpeter with 98 per cent probability, and consistent with the Chabrier IMF and IMFs between the two. This result is consistent with previous studies of spiral galaxies based on independent techniques. In combination with recent studies of massive early-type galaxies that have favoured a heavier Salpeter-like IMF, this result strengthens the evidence against a universal stellar IMF.