Where is the closest parking lot? Or does the museum have a lot?

The closest lot I likely in the harbor center. You should be able to find closer street parking though.

You can find all the parking options here: https://exploreandmore.org/where-to-park/

There is a pay lot directly across the street.

I think we used the 70 Pearl St parking. Street parking is tough to find and you need an app to pay for it. I found the garage had a good rate for the day