1 tablespoon finely chopped parsley, plus more for garnish
Set up a large ice bath. In a pot of boiling water, blanch the lobsters for 3 minutes, until bright red but still undercooked. Using tongs, transfer the lobsters to the ice bath to cool, then drain.
Twist the bodies from the lobster tails. Using scissors, cut along the underside of the tails and remove the meat. Halve the tails lengthwise and discard the dark intestinal veins. Crack the claws and legs and remove the meat. Cut all of the lobster into 1 1/2-inch pieces. Transfer to a plate and refrigerate until chilled.
Squeeze the juice from the lemon halves into a large bowl of water. Working with 1 artichoke at a time, snap off the dark green outer leaves. Using a serrated knife, cut off all but 3/4 inch of the remaining leaves. Peel and trim the bottom and stem of the artichoke. Halve the artichoke and scoop out the furry choke with a spoon. Cut the artichoke halves in thirds and rub with the lemon. Add both the artichokes and the lemon halves to the lemon water.
In a large skillet, melt 1 tablespoon of the butter in 2 tablespoons of the olive oil. Drain the artichokes and pat dry. Add them to the skillet and season with a generous pinch each of salt and pepper. Cook over moderate heat, undisturbed, until well browned on the bottom, about 7 minutes. Turn the artichokes and cook, tossing occasionally, until tender, about 7 minutes longer. Transfer the artichokes to a plate and wipe out the skillet.
In a large bowl, whisk the flour with the curry powder and season with salt and pepper. Dredge the lobster pieces in the seasoned flour, shaking off the excess, and transfer to a plate. In the large skillet, melt 2 tablespoons of the butter in the remaining 2 tablespoons of olive oil. Add the lobster and cook over moderately high heat, turning once, until golden, 3 to 4 minutes. Transfer the lobster to paper towels to drain. Add the shallot and garlic to the skillet and cook over moderate heat, stirring, until softened, about 1 minute. Add the wine and cook, scraping up any browned bits from the bottom of the pan, until evaporated, about 2 minutes. Add the chicken stock and lemon juice and simmer until reduced to 3/4 cup, 2 to 3 minutes. Remove from the heat and whisk in the 1 tablespoon of parsley and the remaining 1 tablespoon of butter. Season the sauce with salt and pepper.
To serve, spoon some of the sauce onto 4 plates and arrange the artichokes and lobster on top. Drizzle with the remaining sauce, garnish with parsley and serve.