Back in 2005, I visited C90 - the Chicago Tracon, and I had to apply 4 weeks before the visit in order to get a clearance from FAA HQ. I submitted the request through the NATCA N90 representative (thanks John
) and I was allowed to make a 1 hour visit of the ops room. However, I had also inquired about a visit to ORD TWR, but was told that TWR visit were not allowed at the time. I am a non-US citizen atco, and I had to fill out the request form (sent to me by the NATCA rep) and I also had to provide a copy of my passport. Sekos, you should definitely go through the NATCA rep at LAX, and if unable to get approval for the TWR, ask for the TRACON.
cheers