CARGO ACR FAILS TO REGARD NOTAM; TAKES OFF ON CLOSED PORTION OF RWY.

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AFTER RECEIVING TAXI INSTRUCTIONS TO RWY 22R VIA 'X;' WE BEGAN OUR TAXI. UPON REACHING THE END OF 'X' WE USED 'ZA' TO THE END OF 22R; WHICH WAS AN AREA OF DISPLACED THRESHOLD. UPON BEING CLRED FOR TKOF; WE TAXIED INTO POS AND NOTICED SOME RED RWY END LIGHTS APPROX 500 FT IN FRONT OF US. WE FELT THEY WERE RECESSED INTO THE RWY AND THE TKOF COULD BE CONTINUED SAFELY. THE LIGHTS WERE WIDE ENOUGH FOR US TO GET BTWN THEM AND; AS WE PASSED THEM ON TKOF ROLL; WE STILL THOUGHT THEY WERE RECESSED. HOWEVER; UPON REVIEWING THE NOTAMS; THEY STATED THE 'NE 800 FT CLOSED FOR RWY 4L-22R.' YET; KNOWING SOMETIMES THAT NOTAMS EXPIRE AND ARE STILL ON THE FLT PAPERS; AND BY THE FACT THAT GND CTL AND LCL CTL SAID NOTHING TO SUBSTANTIATE THE NOTAM; WE PROCEEDED WITH THE TKOF WITHOUT INCIDENT! SUPPLEMENTAL INFO FROM ACN 254493: ZA; PUTS THE ACFT ON THE EXTENDED CTRLINE OVERRUN FOR TKOF POS. AFTER LOOKING OVER FIELD NOTAMS; IT WAS NOTED '800 FT NE OF RWY 22R CLOSED.' WAS THE NOTAM OUTDATED? INVALID? JUST PRIOR TO OUR DEP; ACR Y WAS CLRED TO RWY 22R VIA ZA; AND CLRED FOR TKOF.