  In Paper I of this series, we showed that the ratio between stripped-envelope
(SE) supernova (SN) and Type II SN rates reveals a significant SE SN deficiency
in galaxies with stellar masses $\lesssim 10^{10}~{\rm M}_\odot$. Here, we test
this result by splitting the volume-limited subsample of the Lick Observatory
Supernova Search (LOSS) SN sample into low- and high-mass galaxies and
comparing the relative rates of various SN types found in them. The LOSS
volume-limited sample contains 180 SNe and SN impostors and is complete for SNe
Ia out to 80 Mpc and core-collapse SNe out to 60 Mpc. All of these transients
were recently reclassified by us in Shivvers et al. (2017). We find that the
relative rates of some types of SNe differ between low- and high-mass galaxies:
SNe Ib and Ic are underrepresented by a factor of ~3 in low-mass galaxies.
These galaxies also contain the only examples of SN 1987A-like SNe in the
sample and host about 9 times as many SN impostors. Normal SNe Ia seem to be
~30\% more common in low-mass galaxies, making these galaxies better sources
for homogeneous SN Ia cosmology samples. The relative rates of SNe IIb are
consistent in both low- and high-mass galaxies. The same is true for broad-line
SNe Ic, although our sample includes only two such objects. The results
presented here are in tension with a similar analysis from the Palomar
Transient Factory, especially as regards SNe IIb.
