MISSED APCH PROC PERFORMED BY A B757-200 FLTCREW ON A VOR APCH FOR RWYS 13L AND 13R WHEN RWY LEAD IN LIGHTS FOR RWY 13R OBSCURED BY A MOVING CLOUD BANK S OF JFK; NY.

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I WAS THE CAPT AND PNF ON ACR X; FLT TO JFK. WE WERE CLRED FOR THE VOR RWY 13L AT JFK. SOMETIME AROUND PASSING THE FAF CRI; THE TWR CLRED US TO CHANGE TO RWY 13R AND CLRED US TO LAND ON RWY 13R. A CLOUD BANK HAD DEVELOPED AND BEGAN TO OBSCURE THE LEAD-IN LIGHTS AND THE THRESHOLD OF RWY 13R. TWR RPTED A LOW ALT WARNING. WE EXECUTED A MISSED APCH. WE WERE VECTORED AROUND FOR AN ILS APCH TO RWY 22L. AN UNEVENTFUL LNDG WAS MADE ON RWY 22L. THERE WERE SEVERAL CONTRIBUTING FACTORS TO THIS INCIDENT. THE FO FLYING THE ACFT GOT BEHIND IN SLOWING THE ACFT FOR LNDG CONFIGN. I BECAME DISTRACTED IN ASSISTING THE CONFIGN AND COULD NOT BE 'OUTSIDE' THE ACFT ENOUGH. THE APCH IS ANGLING WITH A R TURN TO THE RWY. IT IS DIFFICULT TO SEE THE RWYS (PARTICULARLY RWY 13R) FROM THE L SEAT. ALTHOUGH RWY 13L REMAINED CLRLY VISIBLE; THE DEVELOPING CLOUD DECK BEGAN TO OBSCURE RWY 13R AND NECESSITATED A MISSED APCH. SUPPLEMENTAL INFO FROM ACN 580529: I WAS DISTRACTED JUST AS I WAS GOING TO CONFIGURE. SUBSEQUENTLY WE WERE SLOWING AND CONFIGURING WHILE LOOKING FOR THE LEAD-IN LIGHTS. SOME CLOUDS HAD MOVED IN AND HID THE APCH END OF RWY 13R. WE COULD SEE RWY 13L FINE. ABOUT THE TIME I DECIDED TO GO AROUND; THE TWR ISSUED A LOW ALT WARNING. WE CAME BACK AROUND WITH VECTORS AND LANDED ILS RWY 22L UNEVENTFULLY. THE ATIS WAS UPDATED IMMEDIATELY FOLLOWING OUR APCH. THE COMBINATION OF CLOUDS OVER RWY 13R; BEING 20 KTS FAST; AND THE CHANGE FROM RWY 13L TO RWY 13R WHICH DECREASED OUR TIME AND DISTANCE TO LNDG WAS TOO MUCH TO OVERCOME AND RESULTED IN A MISSED APCH. WE HAD RWY 13L IN SIGHT AND SEEMED TO BE AT A GOOD ALT; ON VISUAL GS; FOR RWY 13L WHEN WE GOT THE WARNING.