A DC10-40 WAS DISPATCHED IN NON COMPLIANCE WITH THE #3 FAN REVERSER LOCKED OUT INCORRECTLY. ON REVERSING; THE ACFT INCURRED DAMAGE TO THE COWLING.

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ACFT X FROM ZZZ1 TO ZZZ FOR OVERNIGHT LINE CHK. UPON WALKAROUND; NOTICED #3 ENG THRUST REVERSER AT 10 O'CLOCK POS NOT STOWED CORRECTLY. NOTIFIED LEAD MECH OF PROB AND OPENED THE COWLINGS. LEAD DETERMINES PROB DUE TO SHEARED FLEX SHAFT DRIVE CABLE; WHICH I WAS TOLD LATER. LEAD TOLD MY PARTNER AND I TO DO A LOCKOUT PROC PER MEL. THE JOB WAS TURNED OVER TO US AND THE LEAD INSTRUCTED US WHAT TO DO. ANOTHER CREW CHIEF DROPPED OFF THE MAINT MANUAL REF. THE PRESSURE WAS ON TO DO THE JOB QUICKLY; SINCE THE ACFT WOULD LEAVE IN A FEW HRS TO ZZZ2. WE TRUSTED THE LEAD SINCE HE WAS VERY EXPERIENCED AND COULD SAVE TIME. WE CHKED THE MAINT MANUAL NOW AND THEN FOR ADDITIONAL INFO. WE THOUGHT WE HAD DONE THE JOB CORRECTLY; BUT THE NEXT DAY WE FOUND OUT OTHERWISE. THE PLTS HAD DEPLOYED THE REVERSERS AFTER TOUCHDOWN CAUSING DAMAGE TO THE ENG COWLINGS. ALL 4 LOCKOUT PLATES HAD SHEARED. PRIOR TO DEP FROM LAX; THE PLTS HAD CALLED DAY SHIFT MECHS TO FIND OUT IF THE THRUST REVERSER LEVER HAD TO BE SAFETIED CLOSED. THE MECHS CALLED MAINT CTL AND WERE TOLD NOT TO SAFETY THE LEVER. I AM AFRAID WE TRUSTED OUR LEAD TOO MUCH WHEN WE WERE NOT TOO FAMILIAR WITH THE SYS; INSTEAD OF REVIEWING THE MANUAL PROCS MORE.