B757 CREW HAS LEADING EDGE SLAT ASYMMETRY WARNING; DECLARES EMER AND LANDS WITHOUT FLAPS AFTER FINDING BOOK PROCS CONFUSING; FUEL SHORT AND WX CLOSING IN.

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WE WERE CLRED FOR ILS RWY 25L AT LAX. WX WAS CLR; WITH A 1 DEG TEMP DEWPOINT SPREAD. WE HAD JUST HEARD OVER ATC THAT SAN DIEGO WAS BELOW MINIMUMS AND DISPATCH HAD JUST SENT US DATA FOR USING ONT AS AN ALTERNATE; AS WE WERE DISPATCHED ALTERNATE NONE. WE COULD SEE THE FOG JUST OFFSHORE AT LAX. PASSING FUELER; AT 26 DME; WE WERE SLOWED TO 210 KTS FROM 250 KTS PREVIOUSLY ASSIGNED. PASSING 230 KTS I ASKED FOR FLAPS 1 DEG. WE GOT AN EICAS MESSAGE 'LEADING EDGE SLAT DISAGREE;' AND AN AMBER LEADING EDGE LIGHT. THERE HAD BEEN A PREVIOUS IDENTICAL WRITE-UP THE DAY BEFORE. I CHKED FUEL; WE HAD 12500 LBS. I TOLD THE FO THAT WE WOULD CONTINUE THE APCH; I WOULD FLY AND TALK; HE WOULD DO THE ABNORMAL CHKLIST AND IF WE COMPLETED THE CHKLISTS WITH NO PROBS WE WOULD LAND; OTHERWISE WE WOULD MISS APCH AND WORK IT OUT IN HOLDING. I DECLARED AN EMER WITH APCH; AND WE SWITCHED TO RWY 25R. I FELT OVERLOADED WITH THE MCP SO I DISENGAGED THE AUTOPLT AND FLEW A VISUAL APCH. AT THIS POINT I WAS COMFORTABLE KNOWING THAT EVEN IF I HAD TO LAND NO FLAP/NO SLAT I WOULD BE OK ON THIS 11000 FT RWY; BUT I DID NOT WANT TO GO INTO HOLDING AND WORK THROUGH CHKLISTS ONLY TO HAVE THE FOG ROLL IN AND DO AN ACTUAL IFR APCH OR LAND AT ONTARIO; WHERE I HAD NEVER BEEN BEFORE. I EXTENDED THE LNDG GEAR AND HELD CLEAN MINIMUM MANEUVER SPD. ATC KEPT PUMPING US FOR SOULS ABOARD; AND I COULD HEAR FO SAYING SET VREF 20 KTS AND DO A NO FLAP NO SLAT; WHICH DIDN'T SOUND GOOD. I TOLD ATC TO CALL DISPATCH FOR THAT INFO; WE WERE TOO BUSY. I TOLD FO TO LOOK AT THE BUGS AND THE PLI (PITCH LIMIT INDICATOR); WHICH WAS SITTING MAYBE 5 DEGS ABOVE THE AIRPLANE SYMBOL; AND THAT VREF 20 BUG SPDS WOULDN'T WORK. WHEN HE SAID NO FLAP NO SLAT CHKLIST; SPD VREF 30 PLUS 50; AND WE CAN LAND ON 6500 FT OF RWY. I DIDN'T THINK WE NEEDED TO LAND NO FLAP NO SLAT; BUT I KNEW WE COULD WITHOUT ANY PROB; AND BY NOW WE WERE ON TWR FREQ; ABOUT 10 MI OUT AND STABILIZED ON THE ILS. I LANDED WITH AUTOBRAKES 4 SELECTED. LNDG AND ROLLOUT WERE UNEVENTFUL. THE 'B757 LEADING EDGE SLAT DISAGREE' PROC HAS THE QUESTION; 'IS INDICATED FLAP POS GREATER THAN 20 DEGS.' THE 'NO' ANSWER LEADS YOU TO A BOX IN WHICH LINE 1 READS; 'USE EXISTING FLAPS AND SET VREF 20 FOR LNDG.' I THINK THE WORDING WAS THE SOURCE OF FO'S CONFUSION. IT SOUNDS LIKE THE '...FOR LNDG' PHRASE REFERS TO USING EXISTING FLAPS. IN PREVIOUS WRITE-UP THE CREW HAD SAID THEY PERFORMED A FLAP 1 DEG LNDG; AND MAYBE THEY WERE CONFUSED BY THE SAME THING.