Must I upgrade this bathroom circuit from 15 amps to 20 amps?
GFCI lights and fans


  Naturally, the electricians did not GFCI-protect that light, so I want to move it to the GFCI-protected line coming into the master bath


Naturally.  Lights and fans don't need GFCI protection.  However fans do have a tendency to have minor ground faults.  Is there a reason you want to protect them?  

Keep in mind there's a side effect; if you feed your lights off the same outlet as your bathroom appliance receptacles, and you have a ground fault in an appliance, it will kill your lights.  So you'll be standing there in the dark holding a 400 degree curling iron with no idea of where you can set it down.

Bathroom receptacles must be GFCIs.  Nothing else need be, but you might want to GFCI (or convert to low voltage) lights inside showers. 

Bathroom circuits, grandfathered

If the scope of work does not allow you to easily replace a wiring run, it should be grandfathered, i.e. you are allowed to keep the old run and do the best you can with it.  If the scope of work is large enough to make changing the wire easy, then the grandfathering is broken and you must replace. 

installing a new 15A circuit to a bathroom is Right Out, since obviously, if you can install a new 15A circuit, you can install a new 20A circuit just as easily. 

Bathroom receptacles must be on ...

A bathroom receptacle must be on a 20A circuit that is shared only with other bathroom receptacles (in any number of bathrooms). 

Or, a bathroom receptacle must be on a 20A circuit that serves only loads (of any kind) in this same bathroom.  

Take your pick. 

That said, there's a big problem with either setup.  Almost every heat-making bathroom appliance (hair dryer, curler, straightener) is a 1500W heater.  It would be better if they were higher wattage (they are in Europe), but UL caps them off at 1500W.   You cannot run two 1500W appliances on a 20A circuit. 

So once again, as NEC constantly says, it is a code book of minimum requirements, not a design guide of best practices.   So anybody who puts one (1) 20A receptacle circuit in their bathroom because Code tells you to ought to think again.  This is exactly where a DIYer should use his powers of DIY to build the system that works for you, not do the bare minimum  like a contractor would.