A CPR C550 FLC HAVE AN NMAC WITH A VFR ACFT AS THEY BREAK OUT OF THE OVCST APCHING THE OM ON AN ILS APCH.

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APPROX 20-30 MI E OF THE LAF ARPT AT 9000 FT; CTR ADVISED US THAT THERE WAS VFR TFC PRACTICING AN ILS APCH INTO LAF. BOTH OF US (ME AND THE PNF) DISCUSSED THAT HE MUST; BUT UNDERNEATH THE OVCST AS THE TOPS WERE 4300 FT MSL. WE WERE BEING VECTORED ON A R DOWNWIND TO INTERCEPT THE LOC. DUE TO THE WX CONDITIONS AND NO SPD RESTR GIVEN BY CTR WE HELD OUR SPD AT 250 KTS UNTIL ABEAM EARLE (THE OM) AND THEN BEGAN TO SLOW IN ANTICIPATION OF A TURN FOR THE INTERCEPT. WE WERE TAKEN OUTSIDE OF THE MARKER BY ABOUT 10 MI WHEN WE WERE GIVEN A TURN AND DSCNT FROM 5000 FT TO 3000 FT AND CLRED FOR THE ILS RWY 10 APCH INTO LAF. ABOUT 3 MI OUTSIDE THE MARKER WE WERE INSTRUCTED TO CONTACT THE TWR. WE WERE COUPLED ON THE APCH UNTIL THIS POINT AND WERE ON THE LOC AND GS IN A LNDG CONFIGN WITH ONLY REMAINING FLAPS TO GO UNTIL THE LNDG CHKLIST WAS COMPLETED. WITHIN 1/2 MI OF THE MARKER THERE WAS PARTIAL GND CONTACT. IT APPEARED WE WOULD BE VMC IN A MATTER OF MOMENTS. AT THIS POINT THINGS HAPPENED VERY QUICKLY. AS WE BROKE OUT UNDER THE OVCST; AN AIRPLANE BECAME VISIBLE AT OUR 12:30 O'CLOCK; AND 1/8 MI POS TRAVELING IN THE SAME DIRECTION AND ONLY SLIGHTLY LOWER THAN WE WERE. IT BECAME EVIDENT THAT WE WOULD MISS HIM; BUT NOT THROUGH ANY ACTION ON OUR PART. HAD WE BEEN ON THE SAME COURSE IT IS MY OPINION WE WOULD HAVE DSNDED UPON HIM. THERE WAS CONVERSATION THAT ENSUED REFLECTING THAT LAF TWR AND THE ACFT PRACTICING THE APCH DID NOT KNOW THE EXACT LOCATION OF OUR WHEREABOUTS. NOT UNTIL WE INFORMED THE TWR WAS ANY ACTION TAKEN TO BEGIN SEPARATION. IN THE MATTER OF SEVERAL SECONDS THE SIT HAD RESOLVED ITSELF.