Heat the oil. Salt and pepper the chicken breasts and saute until done, turning in the pan to cook evenly. Cut each breast into half or thirds.
Cook the broccoli in boiling water for 2-3 minutes, then drain.
Spray or oil a 9x9 pan. Put the broccoli in it. Put the cooked chicken on top of it.
In a small bowl, mix together the soup, milk, mayonnaise, curry powder, lemon juice, and pepper. Spread over the chicken and broccoli. Sprinkle the cheese on top. Sprinkle the bread crumbs on top of that. Spray the crumbs with butter spray or dab a few bits of butter on top.
You can cover and refrigerate until ready to bake for dinner. Uncover and bake at 350 for 30 minutes or so. If you haven't had to refrigerate it, 20 minutes will probably do just fine.