Umm, no, LAX navigation has nothing to do with Century City height limits, maybe Santa Monica airport, but the approach vectors to LAX from the North, Transpac, Trans Atlantic, Hawaii are all 5-8,000 feet ASL. You can park a Burj Khalifa in Century City and not be a LAX hazard...besides there is something called the Santa Monica Mountains just a couple miles north of CC.
Here is a typical approach pattern, you are usually at 4000+ at downtown LA, (around 10nm from LAX) Coming in over the Westside you are higher 5K+ before you loop back to 24l.
https://skyvector.com/files/tpp/1401/pdf/00237IL24L.PDF
Just a couple weeks ago IST-LAX our great circle had us come on on an indentical approach that I have flown on having done Bay Area and PDX to LA routes dozens of times.
Or a typical transpac route from NRT to LAX a year earlier
Nice shot of LAX before the 180 turn looking the other direction coming in from SFO
