AN ACR TAXIES OFF THE RWY AT LGA; WHERE THERE IS NO TXWY. LIGHTING IS INOP.

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WHILE TAXIING CLR AFTER LNDG ON RWY 4 AT LGA AND TOLD TO EXPEDITE CLRING FOR LNDG TFC BEHIND US WE MISSED TXWY 'R' AND TURNED SHORT OF THE TXWY. I BELIEVE THIS WAS CAUSED BY MY ATTEMPT TO GET THE ACFT OFF THE RWY IN A HURRY TO ACCOMMODATE THE ACFT LNDG BEHIND US. CONTRIBUTING TO THIS IS THE FACT THAT TXWY 'R' AT THE DEP END OF RWY 4 IS VERY POORLY LIT. NO TXWY LIGHTS; NO DOUBLE BLUE TXWY INDICATOR LIGHTS. ANOTHER FACTOR IS THAT THE DEP END RWY END IDENTIFIER (RED) LIGHTS ARE SO BRIGHT THAT THEY OBSCURE YOUR VISION AND MAKE TXWY 'R' VERY DIFFICULT TO DISTINGUISH. ALSO; THERE ARE NO RWY EDGE LIGHTS IN THAT LOCATION. NON-STANDARD LIGHTING AND SIGNAGE CAUSED THIS TXWY EXCURSION. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR SAID THAT THERE WAS A NOTAM ON THE ATIS THAT WAS VERY GENERAL STATING THAT NUMEROUS TAXI AND RWY LIGHTS WERE OUT WITH NO SPECIFIC INFO AS TO LOCATION. THE TXWY 'R' IDENT SIGN AS WELL AS THE EDGE LIGHTS WERE IN FACT OUT; MAKING IDENT OF THE TXWY DIFFICULT. THE SURFACE IN THE AREA OF THE EXCURSION SUPPORTED THE ACFT AND NO DAMAGE WAS DONE TO THE ACFT OR ARPT FACILITIES.