Preheat the smoker to 225 degrees F.
In a large Dutch oven (or similar) add the sauce, green pepper, onion, tomato, basil, garlic, and BBQ Rub and stir until combined.
Place the pot on the lower grate of the smoker and add the Italian sausage and ground beef directly on the grate above the pot of sauce.
Close the lid and let smoke for about 2 hours or until the internal temperature of the meats are at 160 degrees F.
Pull everything off of the smoker and raise the temperature to 300 degrees F.
Once cooled slightly, use your hands to pull the meat into pieces and then add to the pot of sauce and stir.
In a medium bowl add the ricotta cheese and egg and mix until well combined, set aside.
In a 9x13 baking dish or aluminum pan, add a decent amount of sauce to the pan and spread to cover the bottom.
Lay a row of lasagna noodles over the sauce (breaking some into smaller pieces if necessary) and add half of the ricotta mixture and spread over the noodles then add some of both the Italian blend cheese and parmesan cheese.
Repeat the layers once more.
Then finish with one layer of noodles, sauce, and more cheese.
Add ¾ cup of water around the edge of the lasagna.
Transfer to the smoker and place on the grate and let bake uncovered for about 20 minutes.
Then cover with foil and let bake for about an hour covered or until hot throughout and the cheeses are melted.
Let rest for about 10 minutes before cutting and serving.