A GFCI controls all the lights in the bathroom

No, that's not normal. Usually the lights are on a separate circuit that's not GFCI protected and the outlets are on a dedicated, GFCI protected circuit.

A GFCI receptacle has line and load connections. This is different from an ordinary receptacle that has two sets of screws that are functionally identical (as long as the magic tabs are not removed).

This may have been deliberately installed this way. But it is quite possible it was a retrofit GFCI (which is a good idea - they are important safety devices for bathrooms) and the installer didn't understand that GFCI line/load is not the same as a regular receptacle's two sets of screws.

The one catch is that if ant of the lights or the fan are above the tub/shower then they must also be GFCI protected. Assuming that is not the case:

• Turn off the breaker and make sure power is out (receptacles dead and lights/fan won't turn on)
• Open up the box and pull out the GFCI/breaker. Take pictures, in case anything goes wrong.
• Disconnect the wires from the line and load sides.
• Connect all the hot wires (these are wires that were on brass or black screws, should be black wires but not always) together with a wire nut and add a short 12 AWG black wire as a pigtail and connect that to the hot line screw.
• Connect all the neutral wires (these are wires that were on silver screws, should be white wires but not always) together with a wire nut and add a short 12 AWG white wire as a pigtail and connect that to the neutral line screw.
• Put everything back together and turn on the breaker.
• Verify that the GFCI TEST/RESET buttons work.
• Verify that the receptacles work.
• Verify that lights/fan work and that GFCI TEST does not shut off the lights/fan.

It depends what you mean by "normal".

A "GFCI" isn't just a stupid-expensive receptacle. It's actually a zone of protection that can protect other parts of the circuit.

For instance a GFCI circuit breaker protects the entire circuit.

A GFCI recep obviously has the 2 sockets in the zone of protection (kinda the whole point, eh? :) But it can also protect other parts of the circuit, the way a breaker can.

Doing this is a good thing, generally. It means one GFCI is protecting more stuff than just the 2 sockets. It is efficient use of not-so-cheap assets.

However, protecting lights inside a bathroom is "a bit overkill". Bathroom lights don't generally benefit from GFCI protection (unless they are in the shower, then yes, they do). Losing the lights when the GFCI trips is annoying and even dangerous if it's a hot curler! So those are good reasons not to put lights/fan under GFCI protection. Manassehkatz covers the basics of wiring to select whether a load is inside our outside the GFCI protected zone.

In answer to your question is it normal? As Harper has pointed out "it depends".

NEC 210.11(C)(3) Bathroom Branch Circuits. Such circuits shall have no other outlets. Exception: Where the 20-ampere circuit supplies a single bathroom, outlets for other equipment within the same bathroom shall be permitted to be supplied in accordance with 210.23(A)(1) and (A)(2).

If your Bathroom circuit meets this requirement it is allowed. Otherwise it should only service the bathroom outlets.

If you want to change it because you don't like it then follow manassehkatz's suggestion.

Good luck