1. In a bowl, mix sesame oil, salt, pepper, soy sauce, rice vinegar, and sugar. Set aside.
2. Cut avocado into small cubes and sprinkle with lemon juice.
3. Layer four one-quart jars with rice, avocado, red cabbage, carrots, cucumbers, nori strips, and sesame seeds.
4. Pour sauce evenly over the jars.
5. Serve with extra soy sauce and other favorite sushi toppings such as soy sauce, wasabi, and spicy mayo.