Preheat the oven to 350 degrees F.
Heat the butter in a large saucepan over medium heat. Add the onions and green peppers and cook, stirring occasionally, until they are soft and translucent, about 15 minutes. Add the chicken, pimientos, mushroom soup, and chicken broth. Simmer the mixture until the flavors blend and the sauce thickens slightly, about 5 minutes.
Spoon about 1/3 of the chicken mixture into a medium baking dish. Arrange 2 of the noodles over the chicken; repeat layers of chicken and noodles twice more. Top the lasagna with cheese, cover with aluminum foil and bake for 20 minutes. Uncover and bake until the cheese is nicely browned, about 10 minutes. Remove the lasagna from the oven and allow it to set for 5 minutes, then serve.
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