Preheat the oven to 350 degrees F (175 degrees C).
Layer the green beans, corn and lima beans in a 9x13 inch baking dish. In a medium bowl, whisk together the cream and mayonnaise. When that is blended, stir in the shredded cheese. Spread evenly over the vegetables in the dish.
Bake for 50 minutes in the preheated oven, or until the sauce is bubbling and the top is slightly browned.