The northeast corner of 13th South and State Street will take on a new look later this year when the Lincoln Plaza is completed. Lynn Pinegar and Associates is the architectural firm that designed the 65,000-square-foot retail shopping center where Lincoln Junior High School stood for many years. Construction will begin in two weeks with completion set for late October or early November. A day-care center will occupy 13,000 square feet on the second floor of the east end, and there will be parking for 150 cars. The project developer is Steven K. Clark Lincoln Plaza Development. Ralph Jolivet is the leasing coordinator. The property was originally acquired last year by Stockwell Finance Corp., Santa Barbara, Calif., of which Clark is chief operating officer, and ownership was transferred to Lincoln Plaza Development.