Large Transport
Flight Crew Air Transport Pilot (ATP)
Conflict Airborne Conflict; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Air Traffic Control Separated Traffic; Flight Crew Took Evasive Action
Weather; Procedure
We were departing LAX 24L and had just been handed off to Departure at approximately 500 ft. As the FO checked on with SOCAL I noticed a traffic target ahead of us by less than a mile. We were IMC so I did not have visual contact. As soon as communication was established; SOCAL told the intruding aircraft ahead of us to 'turn left immediately' and then told us to 'Stop your climb; stop your climb.' We were just above 1000 ft and I did not have the autopilot on yet so I leveled off. After we leveled off we were told to turn right to 270. During this  maneuvering we got a 'Don't sink' GPWS. We never did get a TCAS warning but the target was close. I believe [the other aircraft] was a foreign carrier that had turned the wrong way and was right in front of us on departure. Not sure all traffic events can be avoided but had I focused more on flying the airplane and not watching the TCAS target on my ND (Navigation Display) I would  not have got the 'Don't sink' warning.
I observed Aircraft Y depart RWY 25 complex and saw the aircraft was turning right unexpectedly. Simultaneously; I observed a target departing the RWY 24 complex. I reached out to Aircraft Y; radar identified the aircraft; said traffic alert turn right heading 180 immediately and to climb immediately. Then I reached out to Aircraft X; radar identified the aircraft and said stop climb immediately; traffic alert; issued the traffic advisory and turned Aircraft X right heading 270.
An Air Carrier Captain and a Departure Controller reported on a traffic conflict between two aircraft departing LAX in IMC.