Do they have their own parking lot or is it off street parking only?

They have both on-street parking and a parking lot behind the building. It isn't accessible from Washington Street but from the parallel street.

Off-street parking is available in the lot between the library and the Presbyterian Church, accessible from Liberty Street.

I have parked in the lot between the library and the church and have never been ticketed. However, I usually park on the street because it's closer to the downstairs door that I enter to attend public meetings.