Preheat the oven to 450°F. Place the pizza crust on a baking sheet.
Spread the pesto sauce on top of the crust up to 1/2 inch from its edge. Break up the tuna into chunks and distribute them over the sauce; then scatter the beans on top. Sprinkle with the red onion and then the lemon juice. Sprinkle evenly with the fontina and mozzarella.
Bake the pizza until the cheese is melted and just beginning to brown, about 10 minutes. Remove from the oven, transfer to a cutting board, garnish with parsley, and cut into slices.