Can an aerodrome in class G airspace be controlled? Can an aerodrome be controlled, even if the only associated airspace is classified G?

E.g. can such an aerodrome have a control tower with the authority to give takeoff and landing clearances and taxi instructions?

I know the opposite is possible (uncontrolled aerodromes in class D airspace for example).

I am not asking about AFIS aerodromes, since AFIS is not an air traffic control service.

Please provide examples and/or references to ICAO SARPs or national regulations.
An airport in class G airspace can have an operating control tower. This is a case of a towered airport in uncontrolled airspace. The airspace is uncontrolled but tower communication must be established within a certain distance and for use of the airports runways.

There are applicable regulations that address this situation. 14 CFR §91.126 (d) requires pilots to establish and maintain communication with a Class G towered airport before entering a 4 NM radius below 2500 AGL.

As of today, Lake City, Florida (KLCQ) is an example of such an airport, although that will change at some point in the future.