Ceiling Fan/Wiring Issue
Check the last receptacle before the switch, anyway

This sounds like a failed connection at the load-side neutral of the last receptacle, given the voltage readings observed.  My bet is that the receptacles were wired using backstabs, too, so if you pull out the last receptacle in the chain and find it back-stabbed, I'd change it over to pigtails to the side-screws, and then repeat for all the other receptacles in the house even, one circuit at a time, as builder-grade backstabs have a habit of stabbing folks in the back in the way you see here.

The other place I would check would be the junction box.  A wirenut is less likely to fail than a backstab, and the lights aren't going to be nearly as susceptible to brownout as a ceiling fan is (the ceiling fan starting current is probably causing enough voltage drop across the bad connection that the fan simply does not turn, while the bulb's simply going to be a bit dim at most), but it's worth checking while you are in there.