Free Lexington City Directories are available at HathiTrust for Lexington, Fayette County, Kentucky.
City directories contain an alphabetized list of residents with their addresses, spouse’s name, profession, and often a reverse lookup by address. They often contain historical information about a locale and they’ll usually contain a separate business directory.
HathiTrust currently has Lexington City Directories available for free searches.
1927 Lexington City Directory (search only, no images)
1931 Lexington City Directory (search only, no images)