Is the lower mass limit of a neutron star the same as the upper mass limit of a white dwarf? If not, when can a white dwarf be more massive than a neutron star?
No, the two limits are not the same - there is some range of masses that both white dwarfs (WDs) and neutron stars (NSs) can have.

The Chandrasekhar mass limit suggests that WDs cannot be more massive than about $1.4\,M_\odot$.  However, this is true for non-rotating WDs.  Rapidly rotating WDs might be as massive as $2\,M_\odot$.  Accretion in a binary system could both spin up a WD and increase its mass.

NSs that have not undergone accretion are regularly observed with masses around $1.3\,M_\odot$, while NSs who have 'recycled pulsars' have an observed mean mass of $\sim 1.5\,M_\odot$ according to the same paper.