I rarely depart LAX "cold" - I generally plan my itinerary to route into LAX on AA the day of my travel back to Oz so as to access T4 rather than TBIT. Until November 2007 this was always a good idea (especially if headed to MEL).
Now I endeavor to route from MEL or SYD internationally rather than BNE, PER or even ADL, simply due to the availability of the F lounges there.
I will always try to route my travel to/from Europe via HGK rather than SIN or BKK for example, simply due to the nice CX lounges there.
YMMV