Preheat the oven to 350 degrees F. Butter a 2 to 3 quart baking dish.
Steam the broccoli in a large microwave-safe bowl with a splash of water, covered, until crisp-tender, 2-4 minutes. Alternatively, steam it in a saucepan with water over medium-high heat. Drain and set aside.
Fill a large high-sided skillet with about 1 inch water and bring to a boil. Add the chicken and cool until just opaque, about 5 minutes. Drain the chicken and pat dry with paper towels.
Stir together the mushroom soup, mayonnaise, lemon juice and curry powder in a large bowl.
Arrange the broccoli on the bottom of the prepared baking dish, then top with the chicken and then the mushroom mixture. Sprinkle the top with the Cheddar and breadcrumbs.
Dot the top with the butter. Bake until bubbly and golden brown, about 30 minutes.