I don't have any historical sources, but I'll hazard a guess based on some background knowledge.

I'd say that earthquakes are the main reason. That combined with the fact that LA was/is an incredibly expansive place, so it was A) affordable to build 'out' rather than 'up' and B) uneconomical to build big, expensive skyscrapers, especially ones engineered sufficiently to withstand earthquakes. It's a lot easier to buy some cheap land in Orange County, cut down the orange groves, and build a modest, 2 story office building or something than build a massive skyscraper capable of resisting a 7.0 earthquake.

What's more, I think the period of time in which LA developed explains it partially as well. Chicago and New York began building their skyscrapers in the 1890s, a time when populations were still fairly densely packed together and automobiles were not common. So, it made sense that in a large office with lots of employees, you need a central location well-serviced by mass-transit (Manhattan/Downtown Chicago), and in such a location there was limited space. Most of LA's population growth occurred after the 1960s, when highways had already been built, the automobile was widely proliferated, and the people living in LA were widely spread out. You didn't need to locate your place of work necessarily in a central location, especially since mass transit was practically non-existent, making the economic model of skyscrapers less sensible and the model of low-level light industrial/commercial developments more competitive.

Also, for most of LA's history, it lacked the sort of industries/businesses that require skyscrapers in the same way Chicago and New York did, but that's just speculation on my part.