C172 pilot with instructor reported engine roughness and returned to the departure airport. Maintenance personnel suggested the roughness was due to carburetor ice.

Narrative

Refresher lesson of PPL skills with a CFII. On departure from ZZZ we turned on course to ZZZ1. We then did a practice diversion onto a VOR track to ZZZ2. Once on the VOR track for about a mile the instructor changed format to practice slow flight. We were flying at 70 mph (the old Cessna with mpg gauge). Mixture full rich and carb heat on. After two turns the engine started coughing and losing RPM. CFII pushed throttle to full; and the engine was 1900 RPM and dropping. I tried leaning the mixture as on the run up on some recent flights the magnetos were fowling. This brought the engine back to life despite being opposite of the formal procedure. We told Approach we had engine troubles and wanted to return; which they cleared direct with altitude at our discretion. We flew higher than normal at 3000 in case the engine started having issues again; and then descending steeply to Runway XX (a very long runway) and all was well. On return we did paper work with the emergency services and messaged the club to ground the aircraft until mechanics could look at it.The mechanics say that it was carburetor icing; even though the carb heat was on.