  We investigate hard-thermal-loop (HTL) corrections to the final lepton
asymmetry in leptogenesis. To this end we solve the Boltzmann equations with
HTL-corrected rates and CP asymmetries, which we calculated in paper I of this
series. We pay special attention to the influence of the two leptonic
quasiparticles that arise at non-zero temperature. We include only decays and
inverse decays and allow for the lepton modes to be either decoupled from each
other, or to be in chemical equilibrium by some strong interaction, simulating
the interaction with gauge bosons. In two additional cases, we approximate the
full HTL lepton propagators with zero-temperature propagators, where we replace
the zero-temperature mass by the thermal mass of the leptons $m_\ell(T)$ or the
asymptotic mass $\sqrt{2} \, m_\ell(T)$. We compare the final lepton
asymmetries of the four thermal cases and the zero-temperature case for zero,
thermal and dominant initial neutrino abundance. The final lepton asymmetries
of the thermal cases differ considerably from the vacuum case and from each
other in the weak washout regime for zero initial neutrino abundance and in the
intermediate regime for dominant initial neutrino abundance. In the strong
washout regime, the final lepton asymmetry can be enhanced by a factor of two
in the case of strongly interacting lepton modes.
