1. Preheat oven to 425°. Stir together cornbread mix and 2/3 cup milk. Pour batter into a lightly greased 8-inch square pan.
2. Bake at 425° for 15 minutes or until golden brown. Cool on a wire rack 5 minutes or just until warm.
3. Stir together mayonnaise and next 5 ingredients in a large bowl.
4. Crumble cornbread to equal 2 cups. Reserve remaining cornbread for another use. Fold cornbread crumbs and tuna chunks into mayonnaise mixture until well blended. Shape tuna mixture into 8 (3- to 3 1/2-inch) patties.
5. Melt 3 Tbsp. butter with vegetable oil in a large skillet over medium-high heat. Add tuna patties, and cook, in batches, 2 to 3 minutes on each side or until golden brown; drain on paper towels. Serve cakes with Lemon Aïoli.
Note: For testing purposes only, we used Martha White Buttermilk Cornbread Mix and StarKist Tuna Creations Herb & Garlic Chunk Light Tuna.