MIL FGT HAD NMAC WITH VFR SMA IN TFC PATTERN. SEE AND AVOID CONCEPT.

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I WAS WORKING LCL CTL WHEN A FLT OF 2 FGT'S WERE DEPARTING RWY 14 SEBOUND. THE FGT'S ASKED FOR A TACTICAL SPLIT AFTER DEP. THIS WAS APPROVED BY ME. INBOUND WAS AN SMA. I ASKED HIS POS; HE SAID 9 MI S OF THE ARPT. I INSTRUCTED HIM TO ENTER A R DOWNWIND RWY 14; AND RPT DOWNWIND. AT THAT TIME I GAVE HIM TFC OF THE DEPARTING FGT'S. AS THE FGT'S WERE DEPARTING I ASKED THE SMA HIS POS AGAIN AND HE SAID 6 MI S. I TOLD THE FGT'S OF THE TFC TO THE S. THE FGT'S STARTED THEIR TACTICAL SPLIT 1/2 MI FROM THE END OF THE RWY. AGAIN; I TOLD THE SMA OF THE TFC AND HE SAID HE SAW THE FGT PASS UNDER HIM. AT THAT POINT I REALIZED THE SMA WAS ACTUALLY 2 MI SE AND WAS ON A 0 ENTRY TO THE DOWNWIND. THE FGT SAW THE SMA IN ENOUGH TIME TO PASS UNDER HIM. DUE TO THE SMA'S ERRONEOUS RPT; AND MY APPROVAL OF THE TACTICAL SPLIT BASED ON THAT RPT; WE HAD WHAT MIGHT BE CALLED A NEAR MISS. THIS; UNFORTUNATELY; IS NOT AN UNCOMMON INCIDENT AT LMT. THERE ARE MANY TIMES BECAUSE OF ERRONEOUS POS RPTS BY ACFT AND HIGH SPD JET ACFT TRAINING; THAT THIS TYPE OF INCIDENT HAPPENS. AS A TWR CTLR I CAN ONLY BASE MY CTL INSTRUCTIONS ON WHAT I AM TOLD. SUPPLEMENTAL INFO FROM ACN 222030: 1 MI PAST DEP END; MY FGT WAS IN A CLB THROUGH APPROX 5500 FT (1400 FT AGL) AND PASSED NOSE TO NOSE DIRECTLY UNDER AN SMA WITH APPROX 200 FT SEPARATION. TFC WAS NOT CALLED OUT BY TWR. TFC WAS CALLED OUT BY ZSE. WERE IT NOT FOR THIS CALL; WE WOULD NOT HAVE SEEN THE SMA PRE-MERGE AND WE COULD HAVE HIT EACH OTHER.