PA32 INSTRUCTOR AND STUDENT HAVE AN NMAC AT LNS.

Narrative

ACFT #1 WAS IN THE TFC PATTERN; PRACTICING 'TOUCH AND GOES.' WE WERE ON OUR THIRD TRIP AROUND THE PATTERN FOR RWY 31. WE WERE CLRED FOR A TOUCH AND GO WITH INSTRUCTIONS FROM THE TWR TO; 'MAKE L TFC; RPT MIDFIELD DOWNWIND.' FOLLOWING US IN THE TFC PATTERN (AND FOLLOWING US DURING THIS TRIP AROUND THE PATTERN) WAS A CESSNA; ALSO PRACTICING TOUCH AND GOES; THE CESSNA RECEIVED THE SAME INSTRUCTIONS FROM TWR (IE; MAKE L TFC RPT MIDFIELD DOWNWIND); BUT WITH THE FOLLOWING ADDITION; 'FOLLOW THE CHEROKEE TFC AHEAD.' EACH OF THOSE TWR CALLS TO THE CESSNA WAS ANSWERED WITH A REF THAT THE CESSNA; 'HAS THE TFC (US) IN SIGHT.' WE MADE A NORMAL TKOF AND CLBED OUT; AT 80 KTS (APPROX 600-700 FPM) ON THE RWY HDG (RWY 31); UNTIL OUR XWIND TURN WHICH CAME AT ABOUT 1100-1200 FT MSL; WHEN WE TURNED APPROX TO A HDG OF 220 DEGS. WE CONTINUED OUR CLB TO PATTERN ALT OF 1400 FT MSL ON XWIND AND LEVELED OFF AT ABOUT 1450 FT MSL. AT THAT TIME WE HEARD THE CESSNA BEING CLRED FOR DEP; WITH THE TWR INSTRUCTING THE CESSNA BEING CLRED FOR A S DOWNWIND DEP; BUT TO FOLLOW THE CHEROKEE TFC. AT ABOUT 1.2 NM FROM THE ARPT WE TURNED DOWNWIND AND MAINTAINED A HDG OF ABOUT 310 DEGS; AND AN AIRSPD OF 80 KTS. THE STUDENT WAS PERIODICALLY CHKING THE ARPT ENVIRONMENT AND THE INTENDED LNDG RWY SINCE LNS WAS LNDG BOTH RWY 26 (LAHSO) AND RWY 31. AS WE WERE APCHING THE MIDFIELD DOWNWIND POINT AND GETTING READY TO MAKE THE INSTRUCTED RADIO CALL; THE STUDENT NOTICED THE CESSNA HEADING TOWARD OUR FLT PATH AT APPROX THE SAME ALT; BUT APPEARED TO BE IN A PITCH-UP ATTITUDE (CLBING) AND BANKING L (TOWARD A S HDG). WHAT IT APPEARED THE CESSNA DID WAS IMMEDIATELY UPON TKOF FROM RWY 31; IT CONTINUED ITS CLB AND TURNED TOWARD THE DOWNWIND (AND US). IT DID NOT FOLLOW A STANDARD PATTERN; DID NOT 'FOLLOW THE TFC' AS INSTRUCTED; AND TURNED EARLY (WHICH WAS CONFIRMED BY THE TWR CTLR DURING A PHONE CALL AFTERWARD). AT THAT POINT; I (THE FLT INSTRUCTOR) TOOK OVER THE FLT CTLS; REDUCED PWR TO IDLE; INITIATED AN IMMEDIATE DSCNT; AND BEGAN A L TURN AWAY FROM THE CESSNA. I THEN CONTACTED LANCASTER TWR; ASKED WHO THE CESSNA WAS (TWR REFUSED TO PROVIDE ANY DETAILS); RPTED A NEAR-MISS; AND REQUESTED INSTRUCTIONS FOR AN IMMEDIATE LNDG; SHORT APCH; ON RWY 31. I RETURNED TO A DOWNWIND PATTERN/FLT PATH LEVELED OFF AT ABOUT 1000 FT MSL AND FLEW THE REMAINDER OF THE PATTERN; APCH; AND LNDG. THE CTLRS IN THE TWR SAW THE ENTIRE CHAIN OF EVENTS; CONFIRMED THAT THE CESSNA DID NOT FLY AS IT WAS INSTRUCTED; CONFIRMED THE CESSNA 'TURNED OUT TOO EARLY;' AND; 'HE (THE CESSNA) SHOULDN'T HAVE DONE THAT.'