TAM do not fly any international flights ONLY within Bolivia so they do not operate from/to Lima.
There are schedules available that are provided to agencies but to be honest we take little notice of them because they are rarely kept to. I have access to the TAM booking system and we simply look up the required dates and routes as and when we need them and then wait for TAM to call teh night before the flights to reschedule it all anyway then we have to run around trying to find our customers to tell them everything has changed.
One possible way to go from Lima to Santa crux woudl be using a star peru and amaszonas combination (they are partners so can be bought as a single passage) but it would probably involve several changes LIMA - CUSCO-LA PAZ-SANTA CRUZ and that woudl end up costing about the same as taca or lan. Typicalk flight prices for Lima to La Paz are about 600usd , so for santacruz you often just addd 100usd on top of that . Not cheap. From time to time there are flights for around 400usd but these seem less and less common nowdays.