Skyhawk 172/Cutlass 172
Flight Crew Instrument; Flight Crew Flight Instructor; Flight Crew Commercial
Flight Crew Last 90 Days 95; Flight Crew Total 400; Flight Crew Type 400
Situational Awareness; Communication Breakdown; Other / Unknown; Time Pressure
ATC Issue All Types; Conflict Ground Conflict; Critical
Flight Crew Took Evasive Action
Environment - Non Weather Related
Pilot on parallel Runway XXR lost his engine and made a return to my Runway XXL for [a priority] landing. I was given a lineup and wait clearance; followed by a clear for takeoff straight out on XXL. Upon establishing the aircraft on centerline I spotted the incoming aircraft and before I was able to bring it to Tower's attention they cleared us for takeoff. My student read back the clearance and initiated the takeoff. Shortly after our roll started I took the flight controls back and began a sharp right turn to exit XXL on taxiway Charlie as another aircraft had taken our place.We conducted the training flight as planned afterword.
Flight Instructor reported taking evasive action to avoid an aircraft with loss of power returning to field.