Rinse the sushi rice with cold water until the water runs clear. Discard the cloudy water and add 1 1/2 cups of clean water to the rice. Cook the sushi rice in an electric rice cooker. Once the rice is cooked, scoop it out onto a plate and let it cool.
Mix the rice vinegar, sugar, and salt together in a small bowl, ensuring the sugar is dissolved. Add the vinegar mixture to the rice and stir evenly. Set the sushi rice aside.
Chop the Crab Delights and mix them with mayonnaise and lemon juice. Stir to combine well.
Lay the bamboo mat on a flat surface and cover it with plastic wrap. Place a small sheet of nori (3.75 inches x 8 inches or 9.5 cm x 20 cm) on the bottom part. Using a spoon, scoop the rice onto the seaweed and spread it evenly in a thin layer.
Use the back of the spoon to press and flatten the surface of the rice. Sprinkle some toasted sesame seeds on top, then press them onto the rice with the back of the spoon.
Turn the seaweed over. Arrange 4 strips of cucumber, 2 strips of avocado, and the crab on top. Be careful not to overfill. Roll the California Roll using the bamboo mat, ensuring that you pull the sushi rolls tightly. Continue rolling with the bamboo mat until you have a nice, tight roll.
Trim both ends of the sushi rolls with a sharp knife, cutting about 1/2 inch (1 cm) off each end. Wipe the knife to remove any residue and wet it with water before cutting each end. Wipe the knife again and wet it before slicing the sushi rolls into pieces. Each roll should yield about 5–6 pieces of sushi.
Repeat the steps above to make 4 sushi rolls. Arrange the sushi on a plate and serve immediately with soy sauce, wasabi, and pickled ginger.