Season lamb chops generously with salt and pepper, and let them rest on the counter for at least 20 minutes. Heat 2 tablespoons of olive oil in a large skillet over medium-high flame—let it get good and hot. Add chops to pan and brown on one side, about 6 minutes. Transfer briefly to a plate.
Reduce heat to medium. Add artichoke hearts, rosemary and garlic to the pan, drizzling in a little more oil, if needed. Gently stir to combine (being careful to not break up the artichoke heart sections) and return chops to the pan, browned side up, nestling in among the artichoke hearts. Cook for about 5 minutes, occasionally stirring the artichoke mixture to keep it from browning or burning.
Transfer chops to a platter and tent with foil. Stir lemon juice into the artichoke hearts mixture and add butter to pan, stirring to combine as it melts, a minute or two. Spoon artichokes around chops and serve.