ULYSSES is a Python package that calculates the baryon asymmetry produced from leptogenesis in the context of a type-I seesaw mechanism. In this release, the new features include code which solves the Boltzmann equations for low-scale leptogenesis; the complete Boltzmann equations for thermal leptogenesis applying proper quantum statistics without assuming kinetic equilibrium of the right-handed neutrinos; and, primordial black hole-induced leptogenesis. ULYSSES version 2 has the added functionality of a pre-provided script for a two-dimensional grid scan of the parameter space. As before, the emphasis of the code is on user flexibility, rapid evaluation and is publicly available at https://github.com/earlyuniverse/ulysses.