We present the second data release of high-resolution ($\le 0.2$ arcsec) 1.5-GHz radio images of 177 nearby galaxies from the Palomar sample, observed with the e-MERLIN array, as part of the LeMMINGs (Legacy e-MERLIN Multi-band Imaging of Nearby Galaxy Sample) survey. Together with the 103 targets of the first LeMMINGs data release, this represents a complete sample of 280 local active (LINER and Seyfert) and inactive galaxies HII galaxies and Absorption Line Galaxies, ALG). This large program is the deepest radio survey of the local Universe, $\gtrsim$10$^{17.6}$ W Hz$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$, regardless of the host and nuclear type: we detect radio emission $\gtrsim$0.25mJybeam$^{-1}$ for 125/280 galaxies (44.6 per cent) with sizes of typically $\lesssim$100 pc. Of those 125, 106 targets show a core which coincides within 1.2 arcsec with the optical nucleus. Although we observed mostly cores, around one third of the detected galaxies features jetted morphologies. The detected radio core luminosities of the sample range between $\sim$10$^{34}$ and 10$\mathrm{<mrow\; data-mjx-texclass="ORD">40</mrow>}$ erg s$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$. LINERs and Seyferts are the most luminous sources, whereas HII galaxies are the least. LINERs show FRI-like core-brightened radio structures, while Seyferts reveal the highest fraction of symmetric morphologies. The majority of HII galaxies have single radio core or complex extended structures, which probably conceal a nuclear starburst and/or a weak active nucleus (seven of them show clear jets). ALGs, which are typically found in evolved ellipticals, although the least numerous, exhibit on average the most luminous radio structures, similar to LINERs.