Heat olive oil in a saucepan over medium-high heat. Add in onion, bell pepper, and celery. Saute until tender, about 5 minutes.
Add in garlic and cajun seasoning. Toast 1 minute. Pour in crushed tomatoes, tomato paste, and sugar. Bring to a boil. Reduce heat to low and simmer 10 to 15 minutes.
In a mixing bowl, combine cheddar, jack, and mozzarella cheese. Toss to combine. In another mixing bowl, combine ricotta, parmesan, eggs, cajun seasoning, and a handful of the shredded cheese mixture. Stir well to combine.
Chop the shrimp so that it is in small pieces. Transfer to a mixing bowl and toss with cajun seasoning.
Assemble lasagna: spread a large spoonful of sauce to cover the bottom of a lightly greased 9x13 pan. Create a layer of the lasagna noodles, overlapping each noodle about 1 inch. Cover with 1/3 of the sauce. Spread half of the ricotta mixture on top. Top with half of the shrimp, and a handful of the shredded cheese. Repeat, creating another layer of noodles, sauce, ricotta, shrimp, and cheese. Top with a final layer of noodles, the remainder of the sauce, and the remainder of the shredded cheese.
Cover the pan with foil and bake in a 375 degree oven for 40 minutes. Remove foil and cook another 20 minutes until cheese is hot and bubbling.