A Tower Controller reported they issued a landing clearance to a departing aircraft which encountered engine failure and requested special handling even though there was another departing aircraft on the runway.

Narrative

Today at XA50Z I was working the LC (Local Control) 2 position at ZZZ ATCT. Aircraft X called ready to depart Runway XXR; I cleared them to depart Runway XXR for a north east departure. Once Aircraft X was rolling on Runway XXR I put Aircraft Y in LUAW on Runway XXR. Aircraft X was approximately 1/2 mile upwind when I observed them in a hard left hand bank appearing to make a westbound turn so I immediately started coordination with the LC1 controller. At this time Aircraft X [requested priority handling] and advised their engine was out. Aircraft X appeared to be turning back toward the runway.I knew that I had an aircraft in LUAW however I prioritized the Aircraft X ahead of the LUAW aircraft and cleared Aircraft X to land on Runway XXL with the intention of exiting Aircraft Y at XX which they would have had plenty of time to do because of XX's close proximity to the end of the runway. Aircraft X made a westbound turn toward the west Runway XYL/XYR. At this time exiting the aircraft in LUAW became a lower priority and I advised them to taxi down the Runway to XY intersection to exit as I cleared Aircraft X to land on Runway XYR after coordinating with the LC1 Controller. At this time Aircraft X regained engine power and flew over the west runway westbound then entered the left downwind for Runway XYL. After coordinating with LC1 I cleared Aircraft X to land Runway XYL and they did without incident. Aircraft Y taxied back to Runway XXR and departed. In this instance I do not have any recommendations; I just needed to explain my reasoning for clearing somebody to land with an aircraft in LUAW on that runway.