AN ACR LGT MADE AN ILS APCH TO THE WRONG RWY UNDER THE DIRECTION OF ZFW. THE SAME FREQ ILS WAS ALIGNED TO THE RWY IN THE OPPOSITE DIRECTION.

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ARRIVED MLU AFTER TWR CLOSED. SINCE NO ATIS; UPDATED WX WITH FSS; CONTACTED ZFW ON 135.1. CTR ASKED INTENTIONS. WE REQUESTED ILS RWY 4. CTR APPROVED AND VECTORED US TO IAF. LOC AND GS FLAGS STAYED IN VIEW UNTIL 15-18 MI FROM FIELD. FLAGS THEN BIASED OUT OF VIEW WITH REVERSE SENSING NOTICED. FO THEN WAS ABLE TO RECEIVE IDENT BUT WAS INCORRECT. WE MAINTAINED 3000 FT AND ABANDONED APCH NEAR OM. DUE TO RAIN OVER VOR; REQUESTED 060 DEG HDG AND CLB TO 5000 FT FROM CTR. WE THEN REALIZED THAT LOC FREQ WAS ALIGNED WITH RWY 22 (SAME FREQ; DIFFERENT IDENT). WE THEN REQUESTED A LONG STRAIGHT-IN TO ILS RWY 22. ZFW SET UP A 25 MI STRAIGHT-IN. ILS AND LNDG UNEVENTFUL MONROE. CORRECTIVE ACTIONS: AIR CREWS NEED TO KNOW WHICH RWY ILS IS LINED UP ON EITHER THROUGH ALL NIGHT ATIS OR ZFW. IN OUR SIT; WINDS (140/6) FAVORED NEITHER RWY. IN ADDITION; USING THE SAME FREQ (109.5) FOR LOC 4 OR 22 WITH SIMILAR IDENTS AND THE RELATIVE WEAKNESS OF SIGNAL STRENGTH ALSO CONTRIBUTED TO A HAZARDOUS SIT. SUPPLEMENTAL INFO FROM ACN 229303: WE WERE UNABLE TO OBTAIN ANY INFO ON MLU ATIS AND WHEN ZFW VECTORED US FOR AN ILS RWY 4 APCH IT REINFORCED MY CHOICE OF RWY 4 AS THE APPROPRIATE RWY. THE FOLLOWING DAY; I CONTACTED THE MLU TWR OPERATOR TO INQUIRE WHAT PROCS THEY FOLLOWED WHEN THEY CLOSED THE TWR OPS. HE STATED THAT THEY TURNED ON THE ILS FOR THE MOST FAVORABLE RWY AT THE TIME OF CLOSING; PUT THAT INFO ON THE ATIS; AND ADVISED ZFW OF THE ALIGNMENT OF THE ILS. INFO AVAILABLE TO ZFW AS TO THE ALIGNMENT OF THE ILS FOR RWY 22 COULD HAVE AVERTED THIS CONFUSION AND POTENTIALLY DANGEROUS SIT.