PDX-LAX is served exclusively by Compass Airline's E175 (American Eagle) so it will always gate at the remote terminal.

50 min is legal connection at LAX but it's really tight!

The bus transfer to T4 will take a minimum of 10 minutes if everything goes smooth - no wait for bus at remote terminal, no aircraft movements at T6, T5 and T4 alley.

Or it could take 30 minutes - wait for bus, stop for aircraft movement at each alley. And you miss the final boarding call and the gate agent gives away your seat to standby.

The only "direct transfer" option will be via the Five Star Service... but in the case of arrival at the remote terminal, it just means they put you in a van instead of the shuttle bus...

https://www.aa.com/i18n/plan-travel/...ivestarservice

I will try calling AA to see if you can reroute you on LAX-LHR that departs later instead of LAX-JFK-LHR.