In a large pot of salted water, boil the broken lasagna noodles according to package directions until al dente. Drain and reserve.
In a medium pot, melt the butter. Once the foaming subsides, add the flour and whisk for about a minute until a roux forms. Add the thyme leaves and whisk another few seconds. Gradually add the milk and keep whisking until a creamy sauce forms, 5 to 8 minutes. Whisk in the lemon juice and season with 1 teaspoon each salt and pepper.
Pour 1/2 cup of the sauce in the bottom of a 12-inch cast-iron skillet. Arrange one-third of the noodles on top, then layer with about 1 cup of the chicken, dollop with half the ricotta, sprinkle with 1/3 of the mozzarella and drizzle another 1 cup of the sauce over the cheese. Repeat with another layer of noodles, chicken, ricotta, mozzarella and sauce. Add a final layer of noodles, mozzarella and sauce. Bake until the cheese is browned and bubbly, about 30 minutes.