Preheat the oven to 350°F (175°C). Lightly grease a 9×13×2-inch baking dish with nonstick cooking spray or butter. Set aside.

Place the chicken breasts in a large pot and cover them with water. Add a pinch of salt, bring to a boil over high heat, then reduce to a gentle simmer. Cook until the chicken is fully tender, approximately 45 minutes. Drain the chicken and allow it to cool before shredding. This step may be done up to 24 hours in advance; store the cooked chicken covered in the refrigerator until ready to use.

Bring a medium pot of salted water to a boil. Add the broccoli florets and cook for 2 to 3 minutes, or until they are bright green and slightly tender. Drain immediately and set aside.

Spread the cooked white rice evenly across the bottom of the prepared baking dish. Layer the blanched broccoli florets on top of the rice.

In a large mixing bowl, combine the condensed cream of chicken soup, sour cream, mayonnaise, lemon juice, shredded chicken, and half of the grated cheddar cheese. Season with salt and freshly ground black pepper to taste. Stir until the mixture is fully combined and evenly blended.

Spoon the chicken mixture evenly over the broccoli and rice layers in the baking dish. Spread it gently with a spatula to ensure an even distribution.

Sprinkle the remaining grated cheddar cheese evenly over the top of the casserole.

Place the dish in the preheated oven and bake uncovered for 40 minutes, or until the cheese is melted and the casserole is hot and bubbling around the edges.

Remove from the oven and allow the dish to rest for 5 minutes before serving. Serve warm.