MLG DEPARTED RWY 24L AND HAD NMAC WITH SMA THAT HAD DEPARTED RWY 25L OR 25R.

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LIFTED OFF RWY 24L AT LAX. AT 600' CONTACTED DEP AND WAS REMINDED TO MAINTAIN 2000' WHICH WAS ASSIGNED ON OUR ORIGINAL ATC CLRNC. AT 1100' I CALLED 1 FOR 2 AND THE COPLT CALLED 'FLAPS UP; CLB PWR.' JUST AFTER PUSHING THE CLB PWR BUTTON ON THE TRI THE LNDG LIGHTS THAT WERE ILLUMINATING THE FOG BEGAN TO ILLUMINATE THE BROADSIDE OF A HIGH WING SINGLE ENG AIRPLANE AT OUR ALT (ABOUT 1450' MSL) MOVING FROM L TO R; S TO N ACROSS MY WINDOW. I GRABBED THE WHEEL PULLED AND TURNED L; AS I DID SO; DEP RPT TFC 12 O'CLOCK LESS THAN A MI AT 2500'. AFTER MISSING THE ACFT I RPTED THE TFC I SAW WAS AT 1450' NOT 2500' AND WE JUST MISSED HIM. THE DEP CTLR SAID THE ACFT WAS IN VIOLATION OF THE TCA AND WAS BEING TRACKED. HAD CURRENT ATIS AT LAX.AFTER PASSING OVER AND BY THE ACFT I RETURNED CONTROL TO THE COPLT WHO CONTINUED THE CLB TO AND LEVELED OFF AT 2000' AS ASSIGNED. THE REMAINDER OF THE FLT TO TUCSON WAS WITHOUT INCIDENT. MY FLT MGMNT REPRESENTATIVE CALLED LOS ANGELES TWR AND WAS TOLD THE SMA HAD TAKEN OFF RWY 25 AT LOS ANGELES AND MADE A TURN N. CALLBACK CONVERSATION WITH RPTR REVEALED FOLLOWING INFO. CALLED RPTR TO SEE IF HIS MGR'S CALL TO LAX DEP CTL PRODUCED ANY USEFUL INFO. HE SAID THAT HE WAS NOT AWARE THAT IT DID. HE COULD NOT TELL ANALYST WHETHER THE SMA HAD TURNED THE WRONG WAY OF IF HE HAD BEEN CLRED TO TURN TO THE N ACROSS HIS TKOF PATH.