As I understand it, LAX (and a slew of others) date from a very old shift from two-letter codes to three-letter codes back in the 40s. In a number of cases, I believe the airports switched codes (usually with a new airport) but in others the codes stuck. PDX, with a similar code situation, dates from 1940. A number of the airports with similarly "logical" codes (MIA, TPA, etc.) are also pretty old (Miami predates WW2, Tampa back to the 20s...and I strongly suspect that DCA would have simply been DC back in the 40s).