Preheat your oven to 375 degrees. Add 1/4 cup of lard to a small pan and preheat over medium heat (about 350 degrees).
Once the lard is hot, fry the tortillas one-by-one, without letting the edges get crispy. About 15 seconds per side. Drain on paper towels and blot with another.
Pour off all but about a tablespoon of lard, then fry the onions until soft. About 5 minutes. Add the pulled pork, mix well with the onions, and cook until heated through.
Divide the shredded cheese by half, then divide one of the piles of cheese amongst the tortillas. Add about 1/4 cup of the pulled pork/onion mixture to each tortilla. Roll the tortillas up and place seam-side down in the casserole dish. Sprinkle any remaining meat over the top.
Top the enchiladas with 1/2 of the green chile sauce and the remaining half of the cheese (it's okay for the ends on the enchiladas to poke out from the sauce). Cook in the oven for 10 minutes, or until the cheese is completely melted and the sauce is starting to bubble at the edges. Remove from the oven and sprinkle with the chopped cilantro.
To serve, ladle some of the still-hot green chile sauce onto warm plates, then place some of the rolled enchiladas on top.