Tower Controller reported an aircraft on departure had an engine failure and returned for a landing. The situation was further complicated by the need to coordinate with numerous people and the pilots repeated replies to stand by.

Narrative

I was working Local West and had the turn releases. Local Center owned the straight out releases. I cleared Aircraft X for takeoff from Runway XXR and told to turn right heading 295. Everything was read back correctly. I lined up traffic afterwards. Once Aircraft X was at departure end; he [requested priority handling] and informed me that he lost an engine and that he was going straight out. I quickly issued traffic and a caution wake turbulence with a heavy that was two miles south of the field that was straight out off of the center runway. Aircraft X did not climb and when offered any type of turn; he told me to standby. I couldn't get much from the pilot as he was busy and would tell me to standby. Aircraft X continued flying straight out at a low altitude. We stopped all departures on all runways and waited to see what the pilots intentions were. Aircraft X finally informed me he wanted to climb to [9000 ft] and wanted a wide left turn to gain altitude and to then turn right to enter a right downwind. He also informed me he would then like vectors for the approach. I asked him if he was able to maintain his own terrain and obstruction clearance. The pilot said he could and started his climb to enter a right downwind. Once in the downwind; the pilot was willing to take a frequency change to final so they could give him vectors. Once I handed him off to final; there was a small [fire] on the southwest area close to Runway XXR. I sent fire command over to investigate while telling them the emergency would now be landing the center runway. I also had a line of departures at the runway and traffic that checked in late on final. I offered the arrival the option to move to the center runway or I would have to send them around due to the fire. The arrival was able to switch runways and land with no issues. Shortly after; airport ops closed Runway XXR due to the fire. I got approval from airport ops to back taxi down the runway to Taxiway 1 and taxi the line of departures to the center runway. Aircraft X landed the center runway and after inspection was told they were fine to taxi back to the gate.I should have issued more MVA instructions or maybe offered an opposite direction arrival. The winds were 130/11 and I do not think he would have taken it and I do not recall what was on final but being he was at a low altitude; that could have been an option. It was difficult to offer much at the time due to trying to coordinate with the Sup; TRACON; Local Center; fire command; airport ops; arrivals; departures waiting in line; etc. and being told to standby from Aircraft X.