A Tower Ground Controller reported the Local Controller cleared an aircraft for takeoff while another aircraft was taxiing across the runway.

Narrative

I was working GC and coordinated to cross runway XX at [taxiway] 1. LC (training in progress) approved the runway crossing. I instructed Maintenance to cross RWY XX at 1 and turn right on TWY 2 for their engine runs. While I was reading a clearance I heard Local Control clear an aircraft for takeoff but I wasn't sure which runway. I then stopped reading my clearance and started scanning. I then told LC that I was still crossing runway XX and the trainer tried to cancel the takeoff clearance; but they said to 'cancel their landing clearance.' Then the OJTI keyed up and told Company to cancel their takeoff clearance; but I think they used the incorrect call sign. There was also a Company aircraft on final. Then the OJTI issued the cancel takeoff clearance with the correct call sign; and the aircraft turned off the runway. I'm not sure what recommendations to make other that we must all remain vigilant and continue to scan; use team work; and coordinate runway crossings accurately to prevent runway incursions.