I've been to LA twice, and for long enough to observe that it's a racially diverse city, but that's really not at all relevant here. We aren't discussing your perceptions of LA, or mine, or anyone else's. We're discussing the city's actual demographic makeup.
The Census data (at least in the source that I'm using, which is here) doesn't provide a deep enough set of crosstabs for us to work this out very precisely. But we can see unambiguously that 28.7% of the population is "White, not Hispanic." We can also see that 31.9% of the population specifically indicated Mexican origin (the Census asks those identifying a Hispanic ethnicity to further indicate whether they are Mexican, Cuban, Puerto Rican, or Other).
No less an authority than you informed us that Mexicans are white:
From these two categories alone (which are mutually exclusive), LA has a white population of 60.6%, and this doesn't count people who identified as "White, Hispanic" but aren't Mexican and people who identified as "Some Other Race, Hispanic," aren't Mexican, but are racially white. These two groups are small (although the first could potentially be on the order of 10%—we can't get a more accurate figure without the crosstabs). So I'll again acknowledge that my original 70% is probably generous, but it's not off by that much. If you have data to suggest otherwise, I'd love to read it. But otherwise, I don't think there's any point to continuing this conversation.