It's actually quite easy to know with a good degree of certainty what the gate for a departing AA flight will be. Just look at the arrival gate for the inbound. While the inbound/outbound pairing does change based on flight delays and such, this information is updated on the AA app such that the new inbound flight is shown.
This is certainly not foolproof as things could even change last minutes, but the latter is unlikely. The pairing is typically established (IME) as soon as the inbound flight takes off from the US and arrival time can be reasonably well ascertained.
Well... at the risk of sounding rude, which I'm genuinely not intending to do, duh. The point is that until a plane has a gate, it could be any gate, and the early LAX flight could get 5 different gates in 5 days.