DUE TO FAILURE OF RWY LIGHTS AT THE DESTN (JOHN WAYNE ARPT) AMERICAN AIRLINE FLT 1262 (BAE-146) DIVERTED TO ONTARIO, CA. WHILE EN ROUTE, IT CONVERGED WITH BRITISH AIRWAYS FLT 282 (BOEING 747), WHICH WAS CLIMBING FROM THE LOS ANGELES INTL ARPT ON A FLT TO LONDON, ENGLAND. SUBSEQUENTLY, AN OPNL ERROR OCCURRED WHEN THE ACFT PASSED WITH A HORIZONTAL SEPN OF ABOUT 1.9 MI AT THE SAME ALT. AN INVESTIGATION REVEALED THAT AFTER COAST TRACON RCVD CONTROL OF FLT 1262 FROM LOS ANGELES CENTER. FLT 1262 WAS CLEARED INTO THE AIRSPACE OF LOS ANGELES TRACON WITHOUT PROPER COORDINATION AMONG THE 3 ATC CONTROL FACILITIES. SPECIFICALLY, THERE WAS INCOMPLETE AND MISUNDERSTOOD COORDINATION BETWEEN CTLRS AT LOS ANGELES CENTER AND COAST TRACON; THE HARBOR SECTOR RADAR AND HANDOFF CTLRS AT COAST TRACON FAILED TO COMPLY WITH PROVISIONS OF LTR OF AGREEMENT BETWEEN COAST TRACON AND AJACENT FACILITIES.