Yes, it’s possible to map city-owned vacant lots with minimum dimensions, but since the dimensions are derived from using GIS functions against the parcel map, it’s inaccurate and painstaking.
No, there’s no existing dataset on the number of parking spaces in each parking lot — that I’m aware of. Perhaps when the city collects tax from pay-for parking lot operators this amount is included in the collection/report. I think there are some new aerial survey businesses that have automated methods to count the number of cars in parking lots, and I’m sure they could also count the number of parking stalls using the same computer vision methods.