In the bowl of the food processor, mix together the flour and salt. Cut the lard or shortening into small pieces and add to the flour. Pulse about 10 times, until it is well distributed throughout the flour. Add the warm water and pulse again about 10 more times, until the dough comes together.
Turn out into the mixing bowl and cover with plastic wrap. Set aside to rest for about 2 hours to allow the flour to fully absorb the liquid and soften.
Turn out the dough onto a floured board and knead for about 1 minute. Divide dough into 8 or 10 equal pieces and roll each into a ball.
Warm the griddle over medium heat. Use the tortilla press (or the bottom of a cast iron skillet) to press each dough ball into a tortilla between 2 pieces of wax paper. When the griddle is good and hot, place one tortilla on the griddle, and wait until you see it start to bubble and the bottom start to brown, about 20 seconds. Turn it over and cook for about 15 seconds more. Place the warm tortillas on the platter and cover with a tea towel or place in a tortilla warmer. Continue with the rest of the dough.
Tortillas will keep in a plastic bag in the refrigerator for several days, or you can freeze them for up to 2 months.