C152 flight instructor reported engine malfunction inflight. Returned to departure airport.

Narrative

While climbing through about 1200 ft. AGL on an instruction flight in a C152; the engine suddenly started running 'rough' with a significant drop of engine power; with about 1900 RPM. Working through the relevant checklists did not result in a restoration of power. I decided to return to the airport (ZZZ) and advised ATC about the engine condition and our return to the airport. ATC instructed us to join the right-hand traffic pattern for Runway XX. When we were handed off to ZZZ Tower I [requested priority landing] on Runway XX; since it was not clear how long we would have engine power; and we were barely able to maintain our altitude; any delay seemed undesirable and [requesting priority landing] was the easiest choice. We were cleared to land on Runway XX; and upon reaching the downwind leg I initiated a power-off 180 approach with an uneventful landing. We had followed the local procedures for high elevation (ca. 3300 ft. MSL); i.e.; leaned the mixture for taxi to avoid carbon/lead build-up at the spark plugs. The run-up check resulted in no abnormalities; ca. 75 RPM drops on each magneto; and the engine ran smoothly; we leaned the mixture for 'best power' prior to departure. Upon take-off; the power production of this particular plane has always been on the low side (perhaps 2100-2200 RPM); and on that particular flight it was on the lower end of this range. I was not concerned because the engine ran smoothly; oil temperature and pressure were 'green;' and the take-off RPM seemed normal for this aircraft (especially when considering the high elevation). The 'climb' checklist; which involved checking oil temperature and pressure also indicated no abnormalities. I am thus not sure this situation could have been avoided using the standard checks that pilots can perform prior to the flight.