Begin by reserving 1/2 cup of the mozzarella cheese.
In a bowl, combine remaining mozzarella, ricotta, eggs, Parmesan and 1/2 teaspoon salt.
Cook carrots in microwave for 2 minutes on high. Stir carrots into cheese mixture and set aside.
In a separate bowl, stir remaining ½ teaspoon salt into zucchini.
Spray slow cooker with cooking spray or brush with olive oil. Spread 1/3 sauce on bottom. Gently break 2 noodles to fill and cover bottom. Spread 1 cup cheese mixture over the noodles. Top with 1 cup shredded zucchini followed by 2/3 cup marinara sauce. Repeat with a second layer (2 noodles, 1 cup cheese mixture, 1 cup shredded zucchini and 2/3 cup marinara sauce).
Add a third layer of noodles and top with remaining cheese mixture and zucchini only. Top with noodles and remaining marinara sauce, then sprinkle with the reserved ½ cup mozzarella.
Cover slow cooker and cook lasagna on High for 3 hours. Let stand 15 minutes before serving.