Do you have a place picked out for lunch, or plan to find someplace once you get to Orvieto? There are fewer restaurants at the east end of town, where the train station and funicular are, but you can reach the center by shuttle or by strolling.
Wandering Orvieto at night two years ago, I was surprised to see a sign for an elevator, and then saw doors outside that weren’t being used by anybody. It didn’t occur to me that they might lead down to a parking garage, and there wasn’t any signage to that effect. We had arrived by train earlier that day and used the funicular, but our hotel was on the east end of town, so we walked there, rather than taking the shuttle once we reached the top of the funicular.
Rick Steves’ Orvieto article on this Website says “train passengers disembark and drivers can leave their cars for free. Visitors can then drive or take an elevator or escalator to the medieval upper town. But my preferred mode is joining the locals to climb the town's natural fortress hill on the slick funicular, which deposits riders about a 10-minute walk from the heart of town.”
So seemingly you can drive to the upper town?!? There are elevators and apparently escalators, and perhaps those are quicker and more direct for just having lunch than parking at the station and doing the funicular, which was really crowded the afternoon after we’d checked out and went back down to depart for Rome by train. If you plan to see more of Orvieto than just getting lunch, parking at the station and riding the funicular will give you a fuller time in town.