B767-300 FLT CREW HAS A TRACK AND HDG DEV DURING FINAL APCH TO RWY AT ATL.

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I WAS AT THE CTLS (CAPT) AND WE WERE CLRED FOR THE ILS RWY 27R AT ATLANTA (ATL); SIDESTEP TO LAND ON RWY 27L. NIGHT; THE WX WAS APPROX 2500-2800 FT OVCST WITH GOOD VISIBILITY BELOW. THE WIND WAS OUT OF THE NNW AT ABOUT 38 KTS AT THAT ALT. WHEN WE BROKE OUT; I SAW THE APCH LIGHTS TO RWY 27L. I THOUGHT THEY WERE FOR RWY 27R (THE RWY I WAS FLYING THE APCH TO). THE APCH LIGHTS FOR RWY 27R WERE NOT ON. I DISCONNECTED THE AUTOPLT AND BEGAN THE VISUAL MANEUVER TO THE L. THE FO TUNED IN THE FREQ FOR RWY 27L. WITH MY TURN TO THE L AND THE WIND PUSHING US OVER; IT DIDN'T TAKE LONG TO GET OFF CTRLINE FOR RWY 27L. WE SAW RWY 28 AND INITIALLY THOUGHT THAT WAS RWY 27L (AGAIN; THOSE WERE THE ONLY 2 RWYS WITH APCH LIGHTS ON). ABOUT THE TIME I REALIZED RWY 27R DIDN'T HAVE APCH LIGHTS AND WE WERE OFF; I STARTED THE TURN BACK AND GOT A CALL FROM TWR ASKING WHERE WE WERE GOING. THERE WAS ANOTHER ACFT ON APCH TO RWY 28 AND TWR INITIALLY DIRECTED HIM TO MAKE A TURN TO THE L. HE SAID HE HAD US VISUALLY. AFTER WE TURNED BACK; HE WAS GIVEN THE OPTION OF GOING AROUND OR LNDG. HE SAID IT WAS NO PROB AND LANDED. AFTER LNDG THE TWR ASKED HIM IF HE WANTED TO CALL ON THE PHONE AND TALK ABOUT IT; HE SAID HE HAD US IN SIGHT; NO PROB; AND DIDN'T CARE TO DISCUSS IT FURTHER. AFTER WE LANDED; THE TWR REQUESTED I CALL AND I DID. HE WANTED TO KNOW WHAT HAPPENED AND HE INFORMED ME THAT IT WAS THE THIRD TIME THAT IT HAPPENED THAT NIGHT. I TOLD HIM EXACTLY WHAT HAPPENED AND HOW THE APCH LIGHTS OFF ON RWY 27R CAUSED ME TO TURN. THE BIG ISSUE HERE; IN MY OPINION; IS THE APCH LIGHTING IN USE FOR THESE SIDESTEPS. WHEN WE FLY THESE APCHS AT NIGHT; WE ARE LOOKING FOR APCH LIGHTS TO RWYS. THE ACTUAL RWY LIGHTS ARE HARD TO MAKE OUT WITH ALL THE OTHER LIGHTS ON AROUND. IT'S VERY EASY TO GET PULLED OFF TO ANOTHER RWY. BOTH THE FO AND I THOUGHT THE APCH LIGHTS WE SAW AFTER BREAKING OUT; WERE FOR RWY 27R. WE BOTH MISSED IT.