...I wonder whether the shuttle in "Let That Be" would be sufficiently provisioned.
I mean, the Cheronians apparently aren't humans, but "the most incredible physical specimen of all time" as McCoy puts it. And they live for tens of thousands of years each. Perhaps they don't need to eat quite as much per day as humans? And perhaps shuttlecraft are surprisingly capable of recycling breathing air and water, and possibly also solid wastes. A trip of a few decades might have been but a minor inconvenience for Lokai, if not for the unfortunate damage his stolen shuttle had suffered...
The shuttle was stolen for two weeks according to the episode and he was on or near a "commercial space lane" so it is possible he was re-fueling/re-supplying at different star systems he was hopping until he ran into trouble. But there is also the "will" factor that the Cheron folks have where they can apparently drive a ship where ever they want it go and possibly over the limits (like Bele forcing the Enterprise to move along at Warp 10.) Lokai might have pushed the shuttle too hard leaving his last stop going to Ariannas.