NAVAJO CHIEFTAIN MAKING A VFR APCH TO LUK ARPT. APCH POINTS OUT TFC IN PATTERN JUST PRIOR TO LATE HDOF. NAVAJO MUST MANEUVER TO AVOID TFC TO PREVENT SERIOUS CONFLICT.

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WE WERE ON AN IFR FLT PLAN AND CLRED FOR A VISUAL APCH (STRAIGHT-IN) TO RWY 21L INTO LUK. THE CTLR POINTED OUT TFC TO US THAT WAS ON A R BASE ALSO FOR RWY 21L AND STATED 'BUT HE'S VFR.' MYSELF AND MY COPLT WERE NOT SURE WHAT HE MEANT BY THAT AND THE CTLR SEEMED HESITANT ABOUT WHAT TO DO WITH 2 ACFT CONVERGING TOWARDS THE SAME AIRSPACE. WITHOUT HAVING US DEVIATE; HE SWITCHED US OVER TO TWR; TO WHICH TWR RESPONDED 'YOU DO SEE THIS GUY ON BASE RIGHT?' AND WE ACKNOWLEDGED. WE ALSO TOLD TWR THAT WE WERE MAKING A 360 DEG TURN TO THE L FOR SPACING AND MADE THE TURN. AS WE WERE 90 DEGS INTO OUR TURN; TWR CLRED US FOR RWY 21R; BUT WE STATED WE WERE UNABLE TO COMPLY AND FINISHED OUR TURN AND HAD AN UNEVENTFUL LNDG ON RWY 21L. IF WE DID NOT MAKE THE 360 DEG TURN WE WOULD HAVE ENDED UP IN VERY CLOSE PROX TO THE OTHER ACFT. THE TWR CTLRS SEEMED UPSET WITH CINCINNATI APCH FOR HANDING US OFF SO LATE (FINAL). WE ALSO BELIEVE THAT THE PROB WOULD NOT HAVE EXISTED IF WE WERE HANDED OFF EARLIER FOR THE TWR.