Place lasagna noodles in the bottom of a long pan and pour hot tap water over them until submerged; let soak at least 30 minutes, agitating occasionally so they do not stick together.
In a large bowl, add all ricotta filling ingredients and mix until combined; set the filling aside.
Preheat the oven to 350 degrees F.
Make the Alfredo sauce: melt 5 tablespoons unsalted butter in a large skillet over medium heat, whisk in the all-purpose flour and minced garlic, and cook while stirring for 2 minutes. Reduce heat to low and gradually whisk in the half and half, low sodium chicken broth, and all spices/seasonings.
Bring the sauce to a boil while whisking constantly, then reduce heat to medium and simmer, whisking occasionally, until thickened but not overly thick, about 5 minutes. Remove from heat and whisk in the freshly grated Parmesan cheese until melted. Stir in the shredded Rotisserie chicken until well combined. Add additional milk or chicken broth if needed to thin the sauce.
Lightly grease a deep 9×13 pan. Spread 1 cup Alfredo sauce in the bottom of the prepared pan (the layer will be thin). Place 4 drained noodles lengthwise and part of a 5th noodle on top to cover. Spread with one third of the ricotta cheese mixture and top with 1 cup shredded mozzarella.
Repeat the layers two more times: spread Alfredo sauce (use one third of the remaining Alfredo per layer, about 2 cups), noodles, ricotta mixture, and mozzarella, for a total of 3 complete layers. To finish, top with the remaining third of Alfredo sauce and the remaining mozzarella (1 cup).
Cover the lasagna with foil and bake in the preheated oven for 30 minutes. Remove the foil and bake an additional 30 minutes or until hot and bubbly. Set the oven to broil (550 degrees F) and broil the lasagna until the top is golden in spots, about 3 minutes, watching closely so it does not burn. Let the lasagna stand 15 minutes before slicing.