Imagine the economic decision on that one?
Run a shuttle service that costs something like $500 per day, to be largely underutilized and even then mostly used by passengers who visit a lounge that gets charged to UA at another $50 per visit. I'm sure they're incentivized to offer this great feature! Hah.
Not sure exactly how many international flights UA runs out of LAX: LHR, PVG, NRT, MEL, SYD just to name a few from the top of my head. Why not just move the international flights to TBIT if there are available gates?