DELTA FLT 1605 LANDED ON RWY 25L. AFTER CROSSING RWY 25R, THE LOCAL CONTROLLER INSTRUCTED THE FLT TO CONTACT THE GND CONTROLLER. THE GROUND CONTROLLER INSTRUCTED THE FLT TO TURN WEST ON THE OUTER TAXIWAY. THE CAPT BECAME DISORIENTATED AND INADVERTENTLY REENTERED RWY 25R. HE IMMEDIATELY REALIZED HIS MISTAKE AND EXECUTED A 180 DEG TURN AND EXITED THE RWY. WHEN THE FLT ENTERED RWY 25R, UNITED AIRLINES FLT 14, A DC-10 HAD ALREADY BEGUN ITS TAKEOFF ROLL. THE CAPT ABOARD UAL FLT 14 ELECTED TO CONTINUE ITS TAKEOFF ROLL, ROTATED AND BEGAN ITS CLIMB. UAL FLT 14 CROSSED OVER DELTA FLT 1605 ABOUT 200 FT A.G.L. DELTA'S CAPT REPTD THAT DUE TO HEAVY CONSTRUCTION AT THE TERMINAL AREA HE BECAME DISORIENTATED EVEN THOUGH HE HAD FLOWN AT LAX FOR MANY YEARS. HE ALSO STATED THAT THE RWY 25R SIGN WAS NOT VISIBLE. INVESTIGATORS FOUND THAT THE SIGN HAD BEEN BLOWN OVER. THE FIRST OFFICER REPTD THAT WHILE THE CAPT WAS TAXIING THE ACFT HE WAS BUSY COMPLETING THE AFTER LNDG CHECKLIST.