Make the risotto: Melt butter in a large saucepan over medium-high. Add shallots and cook, stirring occasionally, until tender, about 2 minutes. Add garlic and cook, stirring, until fragrant and light golden, about 30 seconds. Add rice and cook, stirring, until toasted, about 1 minute.
Pour wine into the saucepan and cook, stirring, until evaporated, about 30 seconds. Gradually add broth a ladle or two at a time, stirring, until rice is just tender, about 25 minutes. Stir parmesan and scrape the risotto into a heat proof container. Fold tuna, basil, and lemon zest into the risotto. Season with salt and pepper, if necessary. Refrigerate until well chilled, at least 1 hour.
Make the risotto balls: Gather about 2 rounded tablespoons of the chilled risotto mixture into a ball and press a piece of mozzarella into the center. Reform risotto around mozzarella, so the piece of cheese is fully covered in risotto. Repeat with remaining risotto and cheese.
Prepare breading station with three large mixing bowls: one bowl with panko (breaking up panko with hands into smaller bits), another with the egg; and the third bowl with flour. Coat each risotto ball in flour and shake off excess. Then, dip into egg mixture and then into panko; set aside on a plate.
Heat 3 inches oil to 350° in a large heavy bottomed pot over medium-high heat. Fry balls in batches, turning a few times, until golden, about 3 minutes a batch. Transfer to a paper towel-lined plate. Arrange warm arrancini in a bowl or on a plate and sprinkle with more parmesan and basil leaves and serve warm with marinara sauce for dipping.