Preheat oven to 350 degrees. In a large pot of boiling salted water, cook pasta according to package instructions. Drain; return to pot. In a large skillet, melt butter over medium-high. Add onion and garlic; cook until onion is beginning to soften, 4 minutes. Add kale, cover, and cook until almost tender, about 5 minutes. Transfer to pot with pasta.
Stir in chicken, ricotta, lemon zest, and 1/2 cup Parmesan; season with salt and pepper. Transfer mixture to a 9-by-13-inch baking dish; top with 1/4 cup Parmesan. Bake until top is golden, 30 minutes.