Cook frozen broccoli (fresh broccoli may also be used) in a small amount of boiling water until crisp-tender; drain well.
In a medium bowl, whisk together the cream of chicken soup, mayonnaise, and lemon juice.
Spread a little soup mixture in the bottom of a 9x13-inch baking dish. Arrange broccoli over soup mixture. Arrange cooked chicken on top of broccoli. Spread the rest of the soup mixture over the chicken. Sprinkle with shredded cheddar cheese.
In a small skillet, over medium heat, melt butter and brown bread crumbs. Sprinkle bread crumbs over the top of the casserole.
Bake for 30-45 minutes. Serve over hot cooked rice.