Preheat the oven to 375 degrees and lightly grease an 8x8 baking dish. Cook the lasagna noodles in a large pot of salted boiling water until al dente, then drain and set aside.
Melt the butter in a saucepan over medium heat. Add the minced garlic and cook for one minute until fragrant. Stir in the heavy cream and 1/2 cup of the Parmesan cheese. Simmer gently for 3 to 4 minutes until slightly thickened, then season with salt and black pepper.
In a skillet, cook the sliced mushrooms over medium heat until they release their liquid and turn golden. Add the spinach and cook just until wilted. Remove from heat.
Spread a thin layer of the cream sauce in the baking dish. Add a layer of noodles, then half the ricotta, half the chicken, half the mushroom-spinach mixture, and a sprinkle of mozzarella. Repeat the layers once more, ending with the remaining noodles and sauce.
Top with the remaining mozzarella and Parmesan. Cover with foil and bake for 25 minutes. Remove the foil and bake 10 more minutes until the top is lightly golden. Let rest 10 minutes before slicing.