Spray a large, nonstick skillet with cooking spray and set over medium high heat. Season chicken pieces with salt and pepper and add to pan. Sauté until cooked, and then remove chicken from pan and set aside.
Place skillet back on heat and respray with cooking spray. Add in onion and garlic and sauté until softened, about 2-3 minutes. Add in mushrooms, 1 tbsp rosemary, and salt and pepper. Cook until mushrooms become tender, about 8-10 minutes. Add in spinach and cook until just wilted, and then add in chicken. Cook until chicken is heated through, about 1-2 minutes and set aside.
Melt butter in a small saucepan over medium high heat. Stir in flour to form a roux. Slowly whisk in milk and broth and cook, whisking constantly, until sauce begins to thicken, about 5-8 minutes. Whisk in parmesan, nutmeg, rosemary, and salt & pepper and continue whisking until parmesan has melted into sauce. Remove from heat and set aside.
In a small bowl, combine ricotta with 1/4 cup of the shredded mozzarella.
Spray a 9” x 13” baking dish with cooking spray and start assembly of lasagna. Begin by spreading about 1/2 cup of the sauce on bottom of the pan. Then lay down 1 layer of lasagna noodles. Top with 1/2 of the ricotta mixture. Then top with 1/2 of the chicken mixture. Pour over another 1/2 cup of sauce, and then repeat all layers, ending with the remaining sauce.
Top with remaining mozzarella and lemon zest, and then cover with foil.
Place in oven and bake for about 30-40 minutes, until hot and bubbly. Then remove foil and place back in oven for another 8-10 minutes to brown the top. Let cool for about 10 minutes before serving.