It seems only fitting: With the bones of King Richard III found under a parking lot in Britain, a theater company that performs free Shakespeare plays every summer in a New York parking lot has decided what to stage this year — “Richard III.” The Drilling Company said Wednesday its Shakespeare in the Parking Lot program will feature the tyrant from Aug. 1 to Aug. 17 in the parking lot at Ludlow and Broome streets on Manhattan’s Lower East Side. Says director Hamilton Clancy: “We have known for a long time that parking lots and Shakespeare were connected. Our intention is to bring Richard III back to life in a parking lot.”