Hi Whale,
In your position I would not even consider who is responsible if you are satisfied the Lot is not unclean and have attempted to eradicate, just ask the EC to address at next meeting suggesting the building be treated for pests at the OC expense. It is usually not an expensive exercise. We treat our building in the common areas every few years as a precaution rather than wait until there is an issue with rodents, cockroaches etc. Perhaps you could do the same and also make a special visit to the Lot with the mice? Before they take over the rest of the building? Cause they breed like..well..mice!
Cheers CBF 