In any district in which single-family dwellings or duplexes are permitted, a single-family dwelling or duplex and customary accessory buildings may be erected on any single lot of record at the effective date of adoption or amendment of the ordinance from which this chapter is derived, notwithstanding limitations imposed by other provisions of this chapter, provided erection of such dwellings and buildings is in accordance with all other applicable Village, county, and state regulations. Such lot must be in separate ownership and not of continuous frontage with other lots in the same ownership. This provision shall apply even though such lot fails to meet the requirements for area or width, or both, that are generally applicable in the district, provided that yard dimensions and requirements other than these applying to the area or width, or both, of the lot shall conform to the regulations for the district in which such lot is located. Variance of yard requirements shall be obtained only through the issuance of a variance by the Board of Appeals in accordance with Section 34-61(2).