Heat oil in a Dutch oven over medium heat. Add onion and garlic; cook and stir until tender, 3 to 5 minutes. Stir in crushed tomatoes, tomato sauce, plant-based sausage, meat substitute crumbles, tomato paste, water, 1 tablespoon parsley, sugar, 1/2 teaspoon salt, basil, Italian seasoning, fennel seeds, and black pepper. Bring to a boil, then reduce heat; simmer, covered, stirring occasionally, until thickened, about 1 1/2 hours.

Bring a large pot of lightly salted water to a boil. Cook lasagna noodles in the boiling water, stirring occasionally, until tender yet firm to the bite, 8 to 10 minutes. Drain and rinse noodles with cold water.

Preheat the oven to 375 degrees F (190 degrees C).

Meanwhile, combine ricotta, remaining 2 tablespoons parsley, egg, and remaining 1/2 teaspoon salt in a bowl.

Spread 1/3 tomato sauce mixture in a 9x13-inch baking dish. Arrange 6 noodles lengthwise over sauce. Spread with 1/2 ricotta mixture. Top with 1/3 mozzarella slices. Spoon 1/3 tomato sauce mixture over mozzarella; sprinkle with 1/4 cup Parmesan. Repeat layers; top with remaining mozzarella and Parmesan. Coat a piece of aluminum foil with cooking spray; cover baking dish, coated-side down.

Bake in the preheated oven for 25 minutes. Remove foil; bake until hot and bubbly, about 25 minutes more. Cool 15 minutes before slicing into 12 equal servings.