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After the emperor and vader die, does lando go back to owning the gas mining facility, or does he stay on with his position as general?

In the EU books he does all sorts of ventures and get's recalled to being a General. Ever the one to make a quick credit and because of the constant conflictions in the EU he makes battle droids etc to seel to the New Republic.

so who is in charge of cloud city?

He resumes his pimping duties.

He goes back to Cloud City after RotJ, (like right after), with some Rebel troops to reclaim it from Imperial Rule, and to spread the word of the Emperor's defeat.
Etc., etc.

In the New Jedi Order series, Lando becomes a "General" again, and he invents the YVH Droids-Yuuzhan Vong Hunter Droids, that hunted out and killed Yuuzhan Vong infiltartors in the New Republic.