In a large pot of salted boiling water, cook lasagna noodles until al dente. Drain and transfer to a sheet pan to cool.
Meanwhile, in a large skillet over medium heat, melt butter. Add garlic and cook until fragrant, 1 minute, then add flour and whisk until golden brown, 1 minute more. Pour over milk and season with salt and pepper. Bring to a simmer and let thicken, 2 to 4 minutes. Add Parmesan and stir until creamy. Add shredded chicken, spinach, and artichokes; gently stir to combine, remove from heat.
Assemble Lasagna: Spread a thin layer of the sauce in the bottom of a 13x9-inch baking dish. Top with a layer of lasagna noodles, slightly overlapping each, a layer of ricotta, a layer of the chicken mixture, and a layer of mozzarella. Repeat for three layers, ending with mozzarella.
Cover with foil and bake until warm and bubbly, about 35-40 minutes. Broil until cheese is golden, about 2 minutes more.
Cool 10 minutes before slicing and serving. Enjoy with a fresh garden salad and French bread!