Complex central structures suggest complex evolutionary paths for barred S0 galaxies

We investigate three barred lenticular galaxies (NGC 2681, NGC 3945 and NGC 4371) which were previously reported to have complex central structures but without a detailed structural analysis of these galaxies' high-resolution data. We have therefore performed four- to six-component (pseudo-)bulge/disk/bar/ring/point source) decompositions of the composite (Hubble Space Telescope plus ground-based) surface brightness profiles. We find that NGC 2681 hosts three bars, while NGC 3945 and NGC 4371 are double- and single-barred galaxies, respectively, in agreement with past isophotal analysis. We find that the bulges in these galaxies are compact, and have S\'ersic indices of $n\sim 2.2 - 3.6$ and stellar masses of $M_{*}$ $\sim 0.28\times10^{10} - 1.1\times10^{10} M_{\sun}$. NGC 3945 and NGC 4371 have intermediate-scale `pseudo-bulges' that are well described by a S\'ersic model with low $n \la 0.5$ instead of an exponential ($n=1$) profile as done in the past. We measure emission line fluxes enclosed within 9 different elliptical apertures, finding that NGC 2681 has a LINER-type emission inside $R \sim 3\arcsec$, but the emission line due to star formation is significant when aperture size is increased. In contrast, NGC 3945 and NGC 4371 have composite (AGN plus star forming)- and LINER-type emissions inside and outside $R \sim 2\arcsec$, respectively. Our findings suggest that the three galaxies have experienced a complex evolutionary path. The bulges appear to be consequences of an earlier violent merging event while subsequent disk formation via gas accretion and bar-driven perturbations may account for the build-up of pseudo-bulges, bars, rings and point sources.