Is there a parking lot for this place or do I just need to find public or street parking?

Street parking or lot across street at Marathon.

I've never had a problem finding street parking, but I can see it being more of an issue when Marathon is holding a concert.

Across the street. And on the street!! Unless its an event, you're fine to park with no fees or fear of towing!

The lot across the street is free if you tell the staff that you're going to Third Coast. Some nights there is no staff; you're fine to park at those times as well.