Preheat the oven to 375° F and butter the pan. Cut the lemons in half and squeeze three halves in a bowl full of water.
Clean the artichokes by removing the hardest outer leaves and the tip, cut into wedges and rub the remaining lemon slice on both sides of the artichokes, then place them in the bowl full of acidulated water to slow down the oxidation. Drain and dry.
In a large skillet with a little oil, brown the artichokes over medium-high heat until crisp, about 5 minutes. Pour the vegetable broth and cook for another 5-6 minutes. Add the chopped radicchio, salt and pepper and cook for another two minutes.
Meanwhile, melt the remaining butter in another pan, add the gnocchi and stir for 4 minutes over medium-high heat. Transfer the gnocchi into the pan with the artichokes and radicchio, add the Parmesan and keep stirring. Transfer everything into the saucepan and bake for 1-2 minutes until the top becomes golden, then serve.