A B767 CAPT AND FO LINE THE ACFT FOR TKOF ON THE RWY RT SIDE HITTING LIGHTS AS THE TKOF ROLL BEGAN. TKOF WAS REJECTED AND TAXIED TO THE GATE FOR A TIRE CHANGE.

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WE WERE CLRED INTO POS ON RWY XXR AT ZZZ AND AS I COMPLETED THE TURN ONTO THE RWY; I LINED THE ACFT UP ON WHAT I THOUGHT WAS THE RWY CTRLINE; CONFIRMED BY WHAT I PERCEIVED TO BE THE RWY CTRLINE LIGHTS. WHEN WE WERE LINED UP; THE RELIEF PLT SAID THAT WE WERE NOT LINED UP CORRECTLY. WHILE MY LINE-UP WAS NOT PERFECT; THE FO AND I BOTH THOUGHT THAT THE RELIEF PLT WAS BEING VERY PARTICULAR SINCE; ACCORDING TO MY PERSPECTIVE; THAT THE CTRLINE WAS NO MORE THAN 1 - 1.5 FT R OF THE NOSE. I DON'T RECALL MY EXACT WORDS; BUT I SAID SOMETHING TO THE EFFECT THAT '(NAME) (THE PF) WILL FIX IT ON THE TKOF ROLL;' MEANING THAT HE WOULD MANEUVER TO THE EXACT CTRLINE AS SOON AS WE STARTED TO ROLL. AT SOME POINT VERY EARLY IN THE TKOF ROLL AND BELOW 60 KTS; I REALIZED THAT WE WERE ON THE R SIDE OF THE RWY AND THAT WHAT I THOUGHT WERE THE CTRLINE LIGHTS WERE IN FACT THE RWY EDGE LIGHTS. ONCE REALIZED; I IMMEDIATELY CALLED 'ABORT;' TOOK CTL OF THE AIRPLANE; AND SIMULTANEOUSLY STEERED TO THE CTRLINE AND SLOWED THE ACFT. WE ADVISED TWR OF THE ABORT AND EXITED THE RWY TO ASSESS THE SITUATION. I DID NOT FEEL ANYTHING UNUSUAL OR ANY BUMPS EITHER BEFORE OR DURING THE ABORT. SINCE THERE WAS THE POSSIBILITY THAT WE HAD HIT SOME RWY LIGHTS; WE ADVISED THE TWR OF THIS AND REQUESTED AN INSPECTION OF THE EDGE LIGHTS. A GND VEHICLE INITIALLY RPTED THERE WAS NO DAMAGE; BUT AN ACFT TAXIING BEHIND US SAID THAT HE SAW 2 LIGHTS DAMAGED. WE TAXIED BACK TO THE GATE FOR A MAINT INSPECTION WHICH DISCOVERED 1 R MAIN LNDG GEAR TIRE DAMAGED AND IN NEED OF REPLACEMENT. AFTER INSPECTING THE ACFT AND REPLACING THE TIRE; MAINT SIGNED OFF THE LOGBOOK ITEM AND WE DEPARTED. WE DEPARTED ON RWY XYL WHICH DID NOT; UNFORTUNATELY; AFFORD US THE CHANCE TO RE-EXAMINE THE RWY XXR TKOF AREA TO SEE WHAT VISUAL CUES COULD HAVE PROMPTED ME TO LINE UP ON THE R SIDE. IN RETHINKING THIS EVENT OVER NUMEROUS TIMES; 1 FACTOR COULD HAVE BEEN THE FACT THAT WITH THE DISPLACED THRESHOLD THE WHITE RWY EDGE LIGHTS DID NOT BEGIN UNTIL ABOUT 2500 FT DOWN THE RWY. AT THIS DISTANCE I COULD HAVE MISTAKEN THE EDGE FOR THE CTR. SUPPLEMENTAL INFO FROM ACN 783158: TAXI FROM THE GATE TO RWY XXR WAS UNEVENTFUL AS THE BEFORE TKOF CHKLIST WAS COMPLETED; WE WERE GIVEN CLRNC TO TAXI INTO POS AND HOLD ON RWY XXR. AS WE WERE GIVEN THE PREVIOUS CLRNC; I CLOSED MY TAXI DIAGRAM AND PLACED IT ON TOP OF MY KIT BAG AND CHKED THAT IT WOULD NOT SLIDE DURING TKOF. WHEN I LOOKED BACK OUT OF THE FORWARD WINDOWS; I NOTICED WE WERE LINED UP ON THE R SIDE OF THE RWY; WITH THE NOSEWHEEL A FEW FT L OF THE R SIDE RWY EDGE LIGHTS. I STATED TO THE CREW THAT WE WERE NOT LINED UP RIGHT. THE FO LOOKED BACK AND SAID IT'S OK. WE WERE GIVEN TKOF CLRNC SOON AFTER THAT AND STARTED TO ROLL. I FULLY ANTICIPATED THE FO TO START CORRECTING TOWARDS THE CTRLINE. HOWEVER; THIS DID NOT OCCUR AND I STATED AGAIN WE WERE NOT LINED UP RIGHT. THE CAPT RECOGNIZED THIS; CORRECTED US BACK TOWARDS THE CTRLINE AND IMMEDIATELY ABORTED THE TKOF.