TFC CONFLICT ARISES BTWN PA28 BACK TAXIING ON RWY 22 AFTER LNDG AT LEW AND STUDENT PLT IN C150 ON APCH TO THE SAME RWY.

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FOLLOWING LNDG ROLLOUT ON RWY 4 AT LEW; CALLED INTENT TO BACK-TAXI RWY 4. TURNED TO BACK-TAXI. UNSEEN ACFT CALLED 'WHAT IS THAT (AIRPLANE) DOING ON (RWY) 22?' BELIEVING WE HAD MISSED TFC IN THE PATTERN FOR RWY 22; CALLED 'WOULD CLR ON RWY 17' AND PROCEEDED TO DO SO. NEXT RADIO CALL 'WHAT DO I DO NOW?' THEN OTHER RADIO VOICE 'ACFT X; DIDN'T YOU SEE THAT (AIR)PLANE? YOU JUST CUT OFF A STUDENT ON FIRST SOLO.' I REPLIED 'NO I DID NOT SEE THEM.' CLRED RWY 17 ON E RAMP. WX: WINDS RPTED WHILE INBOUND 150 DEGS AT 5 KTS. CALM WIND RWY AT LEW = RWY 4. HAZE: FORWARD/SLANT RANGE VISIBILITY GENERALLY 30 MI (ESTIMATED) IN HAZE. THIS WAS MY STUDENT'S FIRST EXPOSURE TO COMPLEX ACFT. LANDED LONG DUE TO MISJUDGED FLARE; RECOVERED AND ROLLED OUT. APPROX 800 FT REMAINING; TURNED; CALLED BACK-TAXI. FACTORS: UNCTLED ARPT. HAZE REDUCED VISUAL CONTRAST. SOLO STUDENT IN C150: WHERE WAS HER CFI? SUPERVISION: UNKNOWN. PREPARATION: INDECISIVE; UNCERTAIN ABOUT COURSE OF ACTION PROCS. COULD HAVE INITIATED GAR SOONER; OR TOLD US SHE WAS LNDG ON RWY 17 (OR ANY RWY) -- MULTIPLE RWYS IN USE.