For lemon aioli: Stir mayonnaise, lemon zest, lemon juice, and grated garlic together in a small bowl. Season to taste with salt and pepper. Thin to a drizzling consistency with milk.
For fish: Pat fish dry with a paper towel. Heat olive oil and butter in a skillet over medium-high heat. Sprinkle both sides of cod with Italian seasoning, salt, and pepper.
Add cod to the hot skillet and sear until golden brown on both sides and fish flakes easily with a fork, 3 to 4 minutes per side. Transfer to serving plates, and serve with lemon aioli.