A B777 INTL CREW LOWERED THE LNDG GEAR LATE ON APCH AFTER AN ALL-NIGHT FLT WITH POOR REST ON THE PRECEDING DAY.

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SLEPT UNTIL XA00 IN ZZZZ. WALKED; ATE; TOOK COUPLE-HR NAP UNTIL WAKE-UP. FLEW THROUGH NIGHT WITH NO REST AS MY BREAK HAD CONTINUOUS MODERATE TURB. FATIGUED; WHICH IS AVERAGE FOR THIS FLT. CONDUCTED BRIEF AT TOP OF DSCNT; INCLUDING FLAPS 30 DEGS; AUTOBRAKES 3 DEGS; MISSED; ETC. JUST BEFORE 1500 FT ON VISUAL; WE OVERHEARD ATC SCOLDING ANOTHER ACR FOR TAXIING ON RWY 8L INSTEAD OF TXWY. THEN TWR CLRED ACFT FOR BASE; RIGHT IN FRONT OF OUR NOSE FOR RWY 4L. SOMEHOW BEING TIRED AND DISTR; I FORGOT GEAR. I ASKED FOR FULL FLAPS AND HORN BEEPED. IMMEDIATELY I RECOGNIZED I HAD FORGOTTEN THE GEAR AND CALLED FOR GEAR EXTENSION. I ASKED CAPT IF HE'D LIKE A GAR; BUT BY THIS TIME EVERYTHING HAD 'COME TOGETHER' AND LOOKED GOOD; SO WE LANDED. I COULD EASILY HAVE MADE TXWY K; BUT POPPED OFF BRAKES AND COASTED TO END OF RWY 4R. WE WOUND UP 'WALKING AWAY FROM ANOTHER ONE' WHICH WE DO AFTER EVERY FLT. POSSIBLY NO ONE WOULD EVER KNOW IF I DIDN'T WRITE THIS RPT. IN MY 30TH YR OF FLYING; THIS IS QUITE DISTURBING TO ME. NOT SOMETHING I EVER WANT TO SEE! HAD WE ALL NOT BEEN SO FATIGUED AND DISTR; I DO NOT THINK I WOULD HAVE FORGOTTEN THE GEAR; AND I DO NOT THINK BOTH THE CAPT AND BUNKIE WOULD HAVE LET ME GO SO FAR WITHOUT LOWERING THE GEAR EITHER! EVEN THOUGH HE DIDN'T SAY ANYTHING; I STRONGLY BELIEVE THE BUNKIE ADDED AN EXTRA LAYER OF SAFETY THAT WOULD HAVE PREVENTED US FROM LNDG WITH THE GEAR UP. LESSON LEARNED IS THAT EVEN WITH EASILY OVER 100 YRS FLYING EXPERIENCE IN THE COCKPIT; MISTAKES CAN BE MADE; AND WE NEED TO BE EVER VIGILANT. I WILL DO MY BEST TO NEVER LET THIS HAPPEN AGAIN. SUPPLEMENTAL INFO FROM ACN 682843: LATE IN LOWERING GEAR AND COMPLETING CHKLIST. VERY TIRED; ALL-NIGHT FLT FROM ZZZ-HNL. UNABLE TO GET NAP AT HOTEL PRIOR TO DEP BECAUSE MAIDS MAKE EXCESSIVE NOISE IN HALLS AND ADJACENT ROOMS. DISTR APCHING FAF BY TWR ADMONISHING ANOTHER AIRLINE FLT FOR TAXIING ONTO A RWY WITHOUT THOSE INSTRUCTIONS -- SEVERAL VERY CAUSTIC XMISSIONS BY TWR TO THE ACFT. THEN TWR TOLD US TO LOOK FOR TFC XING BTWN US AND THE RWYS FROM E TO W THAT WOULD BE LNDG ON RWY 4L; IE; THEIR BASE TURN WAS ACROSS THE FINAL APCH COURSE TO RWY 4R. IT TOOK US AWHILE TO SPOT THIS TFC. THESE DISTRS WITH BEING TIRED ALLOWED US TO BE LATE IN FINAL CONFIGN. NO MANDATORY GAR AUTOMATED NOTIFICATIONS WERE SOUNDED OR DISPLAYED; HOWEVER; FOM GUIDANCE OF GEAR DOWN AND FINAL CHK ACCOMPLISHED BY FAF OR 1500 FT WAS VIOLATED. WE DEEMED CONTINUING FOR LNDG WAS A SAFER COURSE OF ACTION THAN TO GO AROUND WITH TIREDNESS AND HIGH TERRAIN TO THE N AND E OF ARPT. LNDG MADE IN NORMAL TOUCHDOWN ZONE; ON SPD.