  We extend the work on thermodynamics of Lorentzian NUTty solutions, by
including simultaneously the effect of rotation and electromagnetic charges.
Due to the fact that Misner strings carry electric charge, and similar to the
non-rotating case, we observe an interesting interplay between the horizon and
asymptotic charges. Namely, upon employing the Euclidean action calculation we
derive two alternative full cohomogeneity first laws, one that includes the
variations of the horizon electric charge and the asymptotic magnetic charge
and another that involves the horizon magnetic charge and the asymptotic
electric charge. When one of the horizon charges vanishes, we obtain the
corresponding "electric" and "magnetic" first laws that are connected by the
electromagnetic duality. We also briefly study the free energy of the
corresponding system.
