C172 PLT AND BE55 HAD AN NMAC IN LUK CLASS D AIRSPACE.

Narrative

I WAS AT 2000 FT MSL; 9 MI TO THE E OF LUNKIN FIELD. I LISTENED TO ATIS AND THEN CALLED THE TWR AT LUK AND RPTED MY POS AND ALT; E OF THE FIELD; AND REQUESTED PERMISSION TO LAND. TWR REQUESTED AN IDENT AND I DID SO. AT THE TIME; WINDS WERE VERY STRONG OUT OF THE W AND I WAS MAKING ONLY ABOUT 60 NM GND SPD AS I STARTED BACK TOWARDS THE ARPT. TWR RPTED RADAR CONTACT AND INSTRUCTED THAT I CALL A 3 MI FINAL FOR RWY 21R. I READ BACK THE INSTRUCTIONS. I STARTED BACK TOWARDS THE FIELD ON A PATH THAT WOULD ENABLE ME TO BE APPROX 3 NM FROM THE ARPT WHEN I REACHED THE APCH FOR RWY 21R I HEARD THE CALL ON THE RADIO 'LUNKIN TWR; BEECH BARON XXXX; 4 MI FINAL; RWY 21L.' REALIZING THAT I WAS IN THAT SAME POS; I STARTED LOOKING FOR THE TFC AS THE TWR CLRED THE BARON TO LAND. ALMOST INSTANTLY AFTER THEIR CLRNC; WE SAW; HEARD AND FELT THE BARON COME OVER OUR TOP AND BANK TO THE R; COMING FROM OUR 5 O'CLOCK POS. BOTH PLT AND PAX ESTIMATE BARON WAS 20-50 ABOVE US. FROM THE TIME I RECEIVED INSTRUCTIONS TO RPT A 3 MI FINAL FOR RWY 21R TO THE TIME THE BARON RPTED HIS POS 4 MI OUT FOR RWY 21L; I DO NOT RECALL ANY RADIO XMISSIONS FROM OTHER ACFT RPTING A POS OR REQUESTING VECTORS OR CLRNC FOR RWY 21L OR RWY 21R. BOTH PLANES LANDED SAFELY DUE TO THE EVASIVE ACTION TAKEN BY BARON PLT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: PLT INDICATED THERE WAS NO ATTEMPT TO POINT OUT TFC TO EACH OTHER. PLT CALLED THE TWR AFTER LNG AND WAS TOLD THE INCIDENT WOULD BE LOOKED INTO. PLT HAS HEARD NOTHING MORE. PLT IS HESITANT TO ASK THE FAA FOR ANYTHING FURTHER. LET SLEEPING DOGS LIE.