If i inhale a bunch of dust, will my lungs somehow clean it out, or does it stay? how long to clean out if so?

Yes: If you inhale dust some of it can be trapped by the hair and mucous membranes, some of it can be exhaled out depending on the particle size, some of it gets trapped by the mucous glands and will be expectorated, some of it forms foreign body granulomas when it gets engulphed by macrophages. As far as the timeframe it may take a few seconds to few weeks. Hope this will answer your question.