INSTRUCTOR WITH STUDENT PLT HAS NMAC WHILE IN TFC PATTERN AT CTLED ARPT.

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WHILE GIVING DUAL INSTRUCTION TO A PRIMARY STUDENT AND MAKING MULTIPLE L CLOSED TFC TOUCH AND GOES ON RWY 21L; AT THE MID-FIELD L DOWNWIND POINT A BARON (BE58) FLEW RIGHT OVER US; HE WAS JUST TURNING ONTO THE DOWNWIND FROM THE MID-FIELD 45 DEG PATTERN ENTRY. FROM OUR PERSPECTIVE; HE WENT FROM OUR 4 O'CLOCK TO OUR 10 O'CLOCK. HIS GEAR WAS IN TRANSIT; HE WAS SO CLOSE THE COCKPIT GOT DARK AS HIS SHADOW PASSED OVER; WE HEARD HIS ENGS. HE WAS IN A DSNDING R TURN. I CAN REMEMBER FEELING LIKE THE GEAR WAS COMING DOWN AT US; BUT IT WAS OVER IN AN INSTANT BEFORE ANY ACTION COULD BE TAKEN. I BELIEVE THAT IF THE BARON PLT HAD SELECTED HIS GEAR DOWN 5 TO 10 SECONDS EARLIER; HE; MY STUDENT; AND I WOULD ALL BE DEAD. HORIZ SEPARATION WAS 0 FEET; VERT SEPARATION WAS LESS THAN 10 FT. IT WAS VERY CLOSE. I RPTED A NEAR MIDAIR TO THE TWR AND LANDED AFTER THE BARON. WE RENDEZVOUSED ON THE RAMP AND A TWR SUPVR ALSO MET WITH US. THE BARON PLT RPTED HE NEVER SAW US. I WILL HAVE THE TWR TAPES PULLED. IT WAS A GOOD VFR SUNDAY AFTERNOON AND THE TWR WORKLOAD WAS A LITTLE HIGH. WE WERE IN L CLOSED TFC DIRECTLY VISIBLE TO THE TWR. THERE WAS NO MYSTERY TO OUR POS. WE WERE RIGHT WHERE WE SHOULD BE. THE BARON PLT FIRST RPTED ABOUT 7 MI SE AND WAS ASKED TO IDENT (TWICE). TWR DID NOT CALL ME AS POTENTIAL TFC FOR HIM NOR DID TWR CALL HIS POS TO US AT ANYTIME. I BELIEVE THE TWR CTLR ERRED IN FAILING TO PROVIDE ANY SEQUENCING OR SEPARATION FOR 2 KNOWN ACFT; THE BARON PLT (SOUL OCCUPANT) FAILED TO SEE US. WE WOULD HAVE TO HAVE BEEN CLRLY VISIBLE; THE BARON WAS IN A BLIND SPOT FOR THE C150; ABOVE AND SLIGHTLY BEHIND. WE DID NOT SEE HIM; NOR WOULD I EXPECT THAT WE WOULD. HE WAS OVERTAKING US. THE XA:50Z SA AT LUK WAS 150 SCATTERED 250 THIN BROKEN 10 MI VISIBILITY 67 DEGS/45 DEGS 210/17 GUSTS 24 AND ALTIMETER AT 29.80. LUNKEN HAS BEEN A NON-FEDERAL CTL TWR FOR ABOUT A YEAR. PROCS ARE MUCH MORE LAXED THAN WHEN IT WAS A FEDERAL TWR. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATES HE HAS LISTENED TO THE TAPES AND THIS IS DEFINITELY A SYS ERROR. CTLR HAS APOLOGIZED PROFUSELY. THE BARON MADE A TEXT BOOK PATTERN ENTRY AND THAT IS THE SECOND TIME CTLR ASKED HIM TO IDENT. THAT IS WHEN CTLR SHOULD HAVE GIVEN A TA BUT DID NOT. THIS IS NOT A RADAR FACILITY BUT THE CTLRS USE THE REPEATER SCOPE FROM GREATER CINCINNATI TO HELP IDENT POS. THE NON FEDERAL TWR HAS BEEN QUITE LAX PRIOR TO THIS INCIDENT. IT SEEMS THEY HAVE REALLY CRACKED DOWN AND BECOME MUCH MORE EFFICIENT SINCE THE INCIDENT. RPTR IS A CORP PLT AS WELL AS INSTRUCTOR AND FLIES FROM LUK. HE HAS SPOKEN WITH FAA AND THE TWR CHIEF AS WELL AS THE CTLR. ALL ARE QUITE AWARE OF THE INCIDENT AND DO NOT WANT A REPEAT. SUPPLEMENTAL INFO FROM ACN 322004: BOTH PLTS WERE OPERATING UNDER VISUAL FLT RULES AND BOTH WERE LOOKING FOR OTHER ACFT; BUT NEITHER SAW THE OTHER. THE POS OF BOTH ACFT WERE KNOWN TO THE TWR BY VIRTUE OF THEIR ANNOUNCED LOCATION; AS WELL AS THE IDENT PROC. WHILE SEE AND BE SEEN IS THE RULE OF THE DAY IN VFR CONDITIONS; CERTAINLY BETTER COM BTWN ACFT AND CTLRS AS WELL AS KEEPING ALERT TO OTHER ACFT IN THE VICINITY; COULD AVOID FUTURE INCIDENTS SUCH AS THIS.