Pat the pork dry and season generously with the salt and pepper.
Heat the oil in a large, heavy pot over medium-high heat. Sear the pork in batches, without crowding the pot, for 2 to 3 minutes per side. Set aside.
In the same pot, add the onion, garlic, ginger, and lemongrass. Cook for 2 to 3 minutes, until fragrant.
Return the pork to the pot along with the coconut milk, stock, fish sauce, brown sugar, and chilies if using.
Bring to a gentle simmer, not a rolling boil. Cover, reduce heat to low, and braise for 2.5 to 3 hours, until the pork shreds easily with two forks.
Skim off excess fat if desired. Stir in the lime juice just before serving.
Garnish with fresh cilantro and serve.