HII clouds are already neutral; they're a mix of free protons and free electrons with (except in very special circumstances) no charge separation at all. No charge separation, no voltage, no lightning.
Protons and electrons do not, contrary to popular belief, instantly recombine into neutral atoms; the actual observed (and theoretically understood) behavior is very complex and depends on three-body effects (an e- and and p+ to combine, and some third atom in the vicinity as a sort of catalyst). Moreover, most HII is in fact very hot, far above the ionization temperature.
This of course is all under the strictest parameters. Lets Assume that the clouds cool at some point and the cooling happens at an uneven rate the electrodynamics of said system would function differently, if said system functioned like a sterling engine. I have one, its neat to watch.
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