Burke Furniture, a family-owned furniture store that has operated in Lexington since 1963, is going out of business. The late William T. and Joann Burke founded the business and turned the operation over to their sons in the 1970s. The store, off Richmond Road at Mount Tabor Road, announced its closing in a letter mailed to customers: "Burke Furniture has been in business at the same location for over 63 years," the letter read.