Add the chicken to a large saucepan with enough water to cover the meat. Cover the pan, and bring to a boil. Then, reduce the heat and allow the pan to simmer for 20 minutes or so, until the chicken is done. Drain the chicken, chop it, and then set it aside.
Omitting any salt or fat, cook the broccoli according to the package direction. Drain it well, and then arrange the broccoli in a 2-quart baking dish coated with vegetable spray. After layering the broccoli, top it with the chicken.
Preheat your oven to 350 degrees F and then, stirring to blend, combine the soups, milk, and lemon juice. Pour the soup mixture over the top of the chicken and broccoli and then sprinkle cheese over the top.