AN AIRBUS A320 ON TKOF HAD THE L ENG FAN COWLING DEPART THE ACFT INCURRING DAMAGE TO THE LEADING EDGE SLATS; PYLON; FUSELAGE AND THE L HORIZ STABILIZER CAUSE UNDER INVESTIGATION.

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I AND ANOTHER MECH WERE ASSIGNED ACFT XYZ; AN A320. WE WERE ASSIGNED 2 TASKS -- VARIABLE STATOR VANES LUBE ON #1 ENG; AND TROUBLESHOOT AND REPAIR A #2 ENG HIGH PRESSURE BLEED MESSAGE. WE ASSISTED EACH OTHER IN OPENING THE L AND R FAN AND REVERSER COWLS ON #1 ENG AND THE L FAN AND REVERSER COWL ON #2 ENG. I BEGAN WORK ON THE #2 ENG WRITE-UP WHILE HE BEGAN THE VARIABLE STATOR VANES LUBE. WHEN THE VARIABLE STATOR VANES LUBE WAS ACCOMPLISHED; I ASSISTED THE MECH IN CLOSING THE COWLS. WE CLOSED AND LATCHED THE REVERSER COWL TOGETHER; AND I CLOSED AND LATCHED THE FAN COWLS; WHILE THE OTHER MECH LEFT THE AREA FOR A MOMENT. HE RETURNED AS I WAS COMPLETING THE LATCHING OF THE COWL. WE THEN BOTH BEGAN WORKING THE #2 ENG FAULT. UPON COMPLETING THIS TASK; WE CLOSED UP #2 ENG AND PERFORMED AN IDLE RUN CHK ON THE ENG. AFTER COMPLETING PAPERWORK AND TURNING IN EQUIP; I RETURNED TO THE ACFT AND PERFORMED A FOD CHK AROUND BOTH ENGS; LOOKING AT THE SECURITY OF THE COWLS (VISUALLY) AND TO MAKE SURE THE AREA WAS CLR OF TOOLS AND EQUIP. A FEW HRS LATER; DURING TKOF; THE #1 ENG FAN COWLS DEPARTED THE ACFT DURING ROTATION. THE FAN COWLS DAMAGED THE PYLON; #1; #2; AND #3 SLATS; THE FUSELAGE OVER THE WING; AND THE L-HAND HORIZ STABILIZER. AFTER THE MAINT WAS COMPLETED; THE ACFT WAS TAXIED TO THE GATE. THE TAXI CREW; THE GATE CAPT; AND THE FLC ALL DID WALKAROUNDS PRIOR TO ACFT DEP. NONE NOTED ANYTHING ABNORMAL (LATCHES HANGING DOWN OR COWLS NOT FLUSH). THE NIGHT AFTER THE INCIDENT; DURING THE INVESTIGATION; FAN COWLS ON SEVERAL ACFT WERE CHKED FOR LATCH TENSION. APPROX 1/2 THE LATCHES WERE FOUND TO BE 5-15 LBS UNDER TENSION PER THE MAINT MANUAL. THE INVESTIGATION IS CONTINUING. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THE COWLING WAS LATCHED WHEN THE ACFT WAS DELIVERED TO THE TERMINAL AND CHKED BY THE TAXI CREW; CAPT AND GATE MECH AND NOTHING ABNORMAL FOUND. THE RPTR SAID THE NEXT NIGHT AFTER THE INCIDENT SEVERAL ACFT WERE CHKED FOR LATCH TENSION AND ABOUT 1/2 WERE FOUND 5-15 LBS UNDER THE TENSION REQUIRED BY THE MAINT MANUAL. THE RPTR SAID THIS INCIDENT WAS STILL UNDER INVESTIGATION. THE RPTR STATED THIS IS A RECURRING EVENT AS 2 PREVIOUS INCIDENTS OF LOSS OF COWLING ARE KNOWN TO THE RPTR.