The term "local government" is used collectively to describe many levels of overlapping government jurisdictions, such as
Different terminology is used in some states (for example, Lousiana has parishes rather than counties), but the general rule is that any government entity below the level of the state or territory is considered a "local" government.
Consolidated bibliography of county histories in fifty States in 1961, consolidated 1935-1961
Directory of state and local history periodicals
Los Angeles is a unique metropolitan area, with both the city and county intertwined together. It can often be difficult to determine whether you need to work with the city government documents or county government documents to find the information you want.