Rinse the sushi rice under cold water until the water runs clear to remove excess starch. Cook the rice according to the rice cooker's instructions, using 1 ¾ cups of water. Once the rice is cooked, transfer it to a large bowl and gently stir in the rice vinegar, sugar, and salt using a wooden spoon or rice paddle. Let the rice cool to room temperature.
In a large bowl, combine the shredded crab, Japanese mayonnaise, sriracha sauce, sesame oil, and lemon juice. Stir until the mixture is well-combined and creamy. Adjust the amount of sriracha sauce for your preferred level of spiciness. Set aside.
Place a sheet of nori, shiny side down, on a bamboo sushi mat. Wet your hands with a bowl of water to prevent the rice from sticking. Spread a thin layer of the cooled sushi rice evenly over the nori, leaving about 1 inch at the top free to seal the roll. Optionally, sprinkle black sesame seeds over the rice for added flavor and texture.
Spoon a generous amount of the spicy crab salad down the center of the rice. Top with a few slices of avocado and julienned cucumber for added freshness and crunch.
Carefully lift the edge of the nori closest to you using the bamboo mat, and begin rolling the sushi tightly. Make sure the filling stays in place as you roll. Once you reach the exposed edge of the nori, wet it with a little water to seal the roll tightly.
Using a sharp knife, slice the roll into bite-sized pieces on a cutting board. Wipe the knife with a damp cloth between cuts to keep it clean and prevent the rice from sticking. Serve your spicy California sushi rolls with soy sauce, pickled ginger, and wasabi.