Where is was West Los Angeles?

Look closely at the official Los Angeles County Map below (from 1888 and entered "according to Act of Congress") and you can see that the southwest corner is labelled "West L.A."

Until 1896 , the city's western edge was where the present-day Hoover Street is located.  Hoover would be named named for Leonce Hoover (nee Huber), a military surgeon in Napoleon’s army who became a vintner after immigrating to Los Angeles – see The Long and Winding Story of the Streets of Los Angeles .
Forty years later, in 1928, the Los Angeles Times reported that West Los Angeles denoted a far larger area miles west:  the “territory lying between Mulholland High Way on the north, National Boulevard and Venice Boulevard on the south and between Fairfax avenue and the Pacific Ocean."  (It’s West Los Angeles Now, Vast Territory Adopts New Name After Survey, and Choice Gets Approval of Whole Area’s Leaders, Los Angeles Times, October 1, 1928.)