Melt 1/4 cup butter in a large skillet over medium heat; add chicken, and sauté until done. Remove chicken from skillet, and set aside.
Cook broccoli in a steamer basket over boiling water 2 minutes or until crisp-tender. Remove from heat; drain well, and set aside.
Melt remaining 1/4 cup butter in skillet over medium heat. Whisk in flour, and cook, whisking constantly, 1 minute. Gradually add milk, and cook, whisking constantly, until thickened and bubbly. Remove from heat, and stir in Swiss cheese, 1/2 cup Parmesan cheese, lemon juice, and salt.
Layer half of chicken, broccoli, and cheese sauce in a lightly greased 11- x 7-inch baking dish. Repeat layer once. Cover and chill casserole up to 8 hours, if desired; remove from refrigerator, and let stand at room temperature 30 minutes before baking.
Bake, covered, at 350° for 20 minutes. Uncover and sprinkle with 2 tablespoons Parmesan cheese, if desired, and bake 5 more minutes.