To make the meat sauce: Heat a 14-inch skillet over medium-high heat.  Add the beef, veal, and pork and cook, stirring as needed, until browned, about 8 minutes.  Add the celery, onion, and garlic and cook for 2 minutes longer.  Stir in the tomatoes, beef broth, salt, pepper, crushed red pepper, oregano, basil, thyme, and sugar and simmer for 5 minutes.  Remove from the heat.  (This sauce can be made up to several days in advance).

Combine the ricotta and the egg in a medium bowl.  Stir in 1/2 cup of the meat sauce.

To assemble the lasagna:  Add 1/2 cup of the sauce to a 6-quart slow cooker.  Arrange 3 lasagna noodles, side by side, on top of the sauce.  Place 6 heaping tablespoons of the ricotta mixture on the noodles and spread it out evenly.  Top the noodles with one-third of the grated mozzarella, one-third of the provolone slices, and one-third of the fresh mozzarella.  Top with 2 cups of the meat sauce.  Make two more layers with out adding the last layer of cheeses, but use all of the sauce.

Cook on low for 4 hours.

Add the reserved cheeses and the Parmesan to the lasagna and replace the lid.  Turn off the slow cooker and allow the cheese to melt and the lasagna to set up by letting it cool for at least 30 minutes before serving.