Prepare piecrust mix according to package directions, except do not roll out. Cover dough; set aside.
In a large skillet cook onion and potato in water, covered, about 7 minutes or until tender. Drain off liquid. Stir in soup, milk, Parmesan cheese, lemon juice, dill weed, and pepper. Cook and stir until mixture is bubbly. Gently stir in frozen mixed vegetables and tuna. Spoon mixture into an ungreased 2-quart casserole.
On a lightly floured surface roll pastry into a circle 2 inches larger than the diameter of the top of the casserole and about 1/8 inch thick. Make 1-inch slits near the center of the pastry. Center pastry over top of casserole, allowing it to hang over edge. Trim pastry 1/2 inch beyond edge of casserole. Turn pastry under; flute to the casserole edge, pressing gently. Brush pastry with beaten egg.
Bake in a 400 degree F oven for 40 to 45 minutes or until crust is golden brown. Serve immediately.