An accessory building in existence on May 6, 1957, when it is located on the same lot as the principal dwelling on May 6, 1957, may be used as a single-family dwelling by a paying tenant, provided that the population density of the lot shall not exceed one family for each 87,120 square feet (two acres) of the area of the lot on which the accessory building is located. Nothing in this subsection shall be deemed to modify the definition of family in § 216-4, for the purpose of computing the population density of the lot on which the accessory building is located.