B737 FLC WERE CHANGED TO THE MITTS ARR FOR LNDG LAX AND DID NOT ENGAGE THE LNAVE AFTER REPROGRAMMING THE FMS; CAUSING A TRACK DEV.

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ON DSCNT INTO LAX ON THE CIVET ONE ARR. ATC RECLRED US TO FLY DIRECT TO SNRKL INTXN AND FLY THE MITTS ONE ARR. ATC ALSO GAVE US AN AIRSPD CHANGE; ALT XING AT SNRKL AND TO DSND VIA THE MITTS ONE ARR. WE QUICKLY REPROGRAMMED THE FMS (LNAV WITH THE NEW ARR). I WENT OFF THE ATC RADIO TO TALK TO COMPANY AND GET A GATE. I WAS HEADS DOWN FOR 2 OR 3 MINS. WHEN I CAME BACK UP TO THE ATC RADIO; I NOTICED WE HAD DRIFTED S OFF COURSE. I HAD THE LOC FOR RWY 24R DIALED UP TO IDENT SNRKL. I NOTICED FULL SCALE DEFLECTION ON MY LOC NEEDLE AND ALMOST FULL-SCALE DEFLECTION ON THE FO'S LNAV CDI. WE HAD BEEN CLRED DIRECT SNRKL AND I WAS NOT SURE HOW FAR S WE WERE OF OUR INTENDED COURSE. DURING THE COURSE OF OUR FMS REPROGRAMMING; THE LNAV HAD BECOME DISENGAGED OR WE HAD NOT RE-ENGAGED IT AFTER PUTTING THE NEW ARR IN. IN ANY CASE; I IMMEDIATELY TURNED THE ACFT R TO INTERCEPT THE ARR AT INTXN S OR JUST PRIOR TO IT. THE APCH CTLR NEVER SAID ANYTHING TO US; SO I DON'T THINK WE HAD ANY TFC CONFLICTS. OBVIOUSLY; THE MORAL OF THE STORY IS; AFTER REPROGRAMMING THE FMS/LNAV; ALWAYS VERIFY THE LNAV IS STILL ENGAGED IF IT IS REQUIRED. THE REST OF THE ARR AND APCH WERE UNEVENTFUL.