Preheat the oven to 350 degrees F (175 degrees C) and arrange rack in the upper third position. Coat a 9x13-inch baking dish with cooking spray.
Melt butter in a large nonstick skillet over medium heat. Add onion, garlic, Italian seasoning, crushed red pepper, and ¾ teaspoon of salt; cook, stirring often, until onions are softened and translucent, about 4 minutes.
Stir in flour and cook, stirring constantly, for 1 minute. Gradually add milk, and cook, stirring constantly, until slightly thickened, about 3 minutes.
Add cream cheese, and remaining 1 teaspoon salt; cook, stirring constantly, until fully combined. Remove from heat and stir in shredded chicken, cooked rice, spinach, lemon juice, and lemon zest until fully combined. Transfer mixture to prepared baking dish and spread in an even layer. Sprinkle evenly with mozzarella and Parmesan.
Bake in the preheated oven until cheese is melted, about 15 minutes. Turn on the broiler and broil until cheese is browned, 2 to 3 minutes.