NEW ORLEANS — Southern Costume Company is going out of business. For 13 years, the company has specialized in theatrical costume rentals, ready-to-wear costume rentals, and Mardi Gras costume manufacturing. Southern Costume’s 9,000-square-foot warehouse at 951 Lafayette Street contains a sewing studio, multiple dressing rooms and office space. Its client list includes movie and TV productions and Mardi Gras krewes. The entire business is for sale, and so is the costume inventory, along with industrial-sized washers and dryers, sewing and embroidery machines, and office furniture.