HDG TRACK DEV IN FLC DEV FROM ATC CLRNC PROC. POTENTIAL CONFLICT WITH LTSS.

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OUR FLT LAX-JFK TOOK OFF RWY 25R ON THE LOOP 9 DEP. PRIOR TO DEP; MAINT NOTIFIED US ABOUT A WRITEUP ABOUT THE THROTTLES HAVING AN EXCESSIVE SPLIT BTWN THE TWO; AND ASKED US TO SEND ENG RPTS IN SPECIFIED CONFIGNS. THE LOOP 9 DEP REQUIRES A TURN TO HDG 235 DEGS UPON REACHING THE 160 DEG RADIAL FROM THE SMO VOR. JUST PRIOR TO REACHING THE RADIAL; WE RECEIVED CLRNC TO CLB TO 13000 FT. AFTER SELECTING CLB MODE ON THE AUTO THROTTLES; THE THROTTLES DID NOT RESPOND INITIALLY. AFTER A SLIGHT DELAY; I MANUALLY ADVANCED THE THROTTLES AND THEY STABILIZED IN CLB MODE. BECAUSE OF THIS DISTR; WE MISSED OUR HDG CHANGE TO 235 DEGS. WE WERE STILL FLYING 250 DEGS AND CLBING THROUGH APPROX 2200 FT WHEN WE RECEIVED A TCASII RESOLUTION; RED ALERT 'MONITOR VERT SPD' AND A MINUS 4 TFC DISPLAYED. ATC REQUESTED THAT WE 'TURN L HDG 235 DEGS.' I LOOKED OUTSIDE AND BEHIND US. TO THE R WAS ANOTHER ACR'S MLG WHICH HAD DEPARTED OFF RWY 24 LAX. IT WAS ABOUT 6000 FT AWAY AND 400 FT BELOW TURNING N AS WE STARTED OUR TURN.