Do they have a parking lot?

Yes

Small lot at 109 w market. There is others very close.

From their FAQ section: "What about parking? Casa Rio has a small lot located at 109 W. Market Street and is open daily. The cost is $10 Sunday - Thursday and $15 Friday - Saturday. The next closest lot is Riverbend Parking Garage located on the same block as Casa Rio at the corner of Commerce Street and Presa Street. Please see their website for pricing information."

Pay lots all around. Good luck parking at casa rio's actual lot. Pretty small.