Preheat the oven to 275ºF. Season the pork very generously with salt and pepper, rubbing the seasonings into the fat and flesh of the meat. Set the roast aside for at least 30 minutes or up to 1 hour to bring to room temperature.
Combine the onions, garlic, thyme, and rosemary in a medium mixing bowl and toss to combine. Heat the vegetable oil in a Dutch oven over medium-high heat. When the oil is very hot, sear the meat on all sides until deeply browned and crusty, 10 to 12 minutes total.
Transfer the meat to a plate, reduce the heat to medium, and then stir in the butter. When the butter has melted, stir in the flour to make a roux and continue to cook, stirring, until the roux turns a dark peanut butter color, about 10 minutes.
Add the onion mixture and cook, stirring, until all the ingredients are well coated and the mixture is thick. Whisk in the chicken broth and bring to a simmer, stirring constantly. Return the pork to the Dutch oven, spoon some of the onion mixture over the meat, cover, and roast for about 3 hours, turning and basting the pork every 30 minutes or so, until the meat will break apart when pressed gently with a fork.
At this point, you can serve the roast right out of the pan, or transfer it to a plate, then simmer the pan drippings, skimming off excess fat, until reduced by about one-third, or until it coats the back of a spoon. Add the lemon juice and taste for seasonings.
Before serving, sprinkle the roast with some additional salt, to taste. Serve the roast smothered with a generous amount of sauce over hot steamed rice.