RPTR EXPERIENCES NMAC.

Narrative

WE HAD JUST COMPLETED AN NDB RWY 27 APCH INTO LNN AND HAD BEEN GIVEN A VECTOR OF 090 DEGS AND MAINTAIN 3000 FT TO BE VECTORED FOR THE SAME APCH AGAIN. WE WERE APPROX 3-4 MI N OF LNN ARPT ABOUT 1/2 -- 1 MI OFF THE SHORELINE OF LAKE ERIE. CLEVELAND APCH WAS PROVIDING THE VECTORING FOR US. WHILE LEVEL AT 3000 FT AND ON THE ASSIGNED VECTOR OF 090 DEGS I NOTICED AN ACFT LNDG LIGHT AT OUR 12 O'CLOCK POS AT ABOUT OUR ALT. CLEVELAND DID NOT ADVISE US OF ANY TFC. BOTH OUR TAXI AND LNDG LIGHTS AS WELL AS OUR STROBE LIGHTS AND BEACON WERE ILLUMINATED THE ENTIRE FLT AND WE WERE ON AN IFR CLRNC. THE TFC HAD NOW APPEARED TO TURN SBOUND AND WOULD NOT BE A HAZARD TO US. THEREFORE; I TOOK MY EYES OFF OF HIM AND MONITORED THE PROCS OF MY STUDENT. ABOUT 15 SECONDS LATER I LOOKED AGAIN FOR THIS TFC AND IT WAS NOW AT OUR 12 O'CLOCK POS AND AT OUR ALT AND A COLLISION WAS IMPENDING IF EVASIVE ACTION WERE NOT TAKEN. I PULLED HARD BACK ON THE CTL WHEEL TO CLB AND TOLD MY STUDENT 'MY AIRPLANE.' WE PASSED SLIGHTLY ABOVE THE OTHER ACFT WHICH APPEARED TO BE SOME TYPE OF HIGH WING CESSNA. I IMMEDIATELY NOTIFIED CLEVELAND APCH THAT WE WERE CLBING DUE TO A 'NEAR MISS' FOR OPPOSITE DIRECTION TFC AT 3000 FT. THE CTLR SAID HE DIDN'T HAVE THAT TFC ON RADAR AND THE ONLY TARGET HE HAD WAS S OF US AT A LOWER ALT (WE HAD THIS TFC IN SIGHT -- IT WAS NO FACTOR). IT IS MY BELIEF THAT THIS OPPOSITE DIRECTION TFC HAD VIOLATED THE CLASS D AIRSPACE OF LNN ARPT AND HAD ITS XPONDER OFF FOR THIS REASON WHICH IS WHY CLEVELAND DID NOT HAVE HIM ON RADAR.