This was once two streets: Laveta Place was laid out in 1887 between Bellevue Avenue and Kensington Road (then more accurately named “The Crescent”, owing to its shape). Laveta Terrace was introduced north of Sunset Boulevard in 1905. The two Lavetas became one in 1912. My guess is that the name comes from la veta, Spanish for “the mineral vein”. In 1887 Los Angeles, many capitalists investing in local real estate also had significant mining interests outside the city, so that could have been the inspiration. I’ll add that La Veta Avenue, a major thoroughfare in the city of Orange, was also named in 1887, so it’s possible that Andrew Glassell, who developed land here and also cofounded Orange, was behind the name – but don’t quote me on that. Other L.A/Orange developers such as Abraham Jacoby and Lewis Thorne might have coined it. In short: I don’t know.