Bring a large pot of salted water to a boil and line a sheet pan with parchment paper. Add lasagna sheets to the pot and cook until al dente. Drain and arrange overlapping on the prepared sheet pan.

In a medium saucepan, melt butter over medium heat. Whisk in flour and cook for 1–2 minutes until lightly golden. Slowly pour in milk while whisking continuously until smooth. Simmer for 4–5 minutes, until slightly thickened. Remove from heat and whisk in Greek yogurt, salt and pepper until creamy.

In a large skillet, heat olive oil over medium heat. Add the onion and cook for about 5 minutes, until softened. Add garlic and cook for 1 minute more. Stir in shredded chicken, spinach, Italian seasoning, salt, and pepper. Cook for 2–3 minutes until heated through and the spinach wilts. Remove from heat and stir in ricotta, Parmesan, eggs, and basil until well combined.

Preheat the oven to 375°F. Spread about 1 ½ cups of the béchamel sauce over the bottom of a 9x13-inch baking dish. Add ⅓ of the pasta, overlapping slightly, followed by half of the chicken-ricotta mixture and about 1 cup of béchamel sauce. Add another layer of pasta, the remaining chicken-ricotta mixture, and another 1 cup of béchamel sauce. Finish with the final layer of pasta, pour the remaining béchamel over the top, and sprinkle with mozzarella and Parmesan cheese.

Cover with foil and bake for 30 minutes. Remove foil and bake for an additional 20 minutes, until the top is golden and bubbly. Let rest for 15 minutes before slicing and serving.