Wash 1 cup rice and bring to boil with 2 1/4 cups water, reduce heat on lowest and simmer for about 45 minutes until water is absorbed. Turn off heat and allow to sit for 15 minutes.
Combine lemon juice, sugar, black sesame seeds and salt.
Add to rice, stir well and set aside to marinate for 5 minutes.
On a bamboo sushi mat, place a sheet of nori with the shiny-side down. Spread rice over nori sheets, leaving a 1/2 inch clear space at the top and bottom.
Arrange red bell pepper, yellow and orange peppers in an even strip horizontally starting from the side nearest you.
Arrange cucumber alongside bell peppers, then arrange avocado slices on top.
Holding the mat and the edge of the nori sheet nearest to you, roll into a cylinder. Use the mat as your guide, roll tightly so that it sticks together and encloses the filling tightly.
Transfer roll seam side down onto a cutting board, use a wet knife to cut each roll into six pieces and stand them into a serving platter.
Garnish with fresh pickled ginger and serve with Ponzu sauce.