Preheat oven to 475 degrees. Set two wire racks on two rimmed baking sheets lined with foil.
In a large bowl, whisk together 1 cup water, 3 eggs, 1 teaspoon salt, and 1/2 teaspoon pepper. Add beef and breadcrumbs and mix well (preferably with your hands).
With wet hands, from the mixture into 1 1/4-inch meatballs (you will have about 65 to 75 meatballs).
Arrange the meatballs on the wire racks and bake until browned, about 20 minutes.
Meanwhile, to a slow cooker add tomato puree, ketchup, remaining 1 cup water, brown sugar, onion, and lime juice. Stir to combine.
Transfer baked meatballs to the slow cooker. Cover and cook until sauce is hot, 3 to 4 hours on HIGH or 6 to 8 hours on LOW. Season to taste with salt and pepper before serving.