For the rice: Place rice in a bowl and rinse with cold water until water is clear. Drain rice in a mesh strainer. In a medium pot combine the rice with 3 cups of water over medium-low heat. Cover and let cook until rice is tender and has absorbed all the water, about 20 minutes. While rice is cooking combine rice wine vinegar and sugar and mix until sugar is dissolved. When rice is done transfer to wooden bowl and add vinegar mixture. Gently mix with a wooden spoon until the rice mixture cools but is still slightly warm. Cover with plastic wrap, set aside and prepare remaining sushi roll ingredients.
For the rolls: In a small bowl toss the avocado gently with the lemon juice. Lay a dry bamboo mat on a work surface so that the slats run horizontally and cover with plastic wrap. Place a piece of the nori on the bamboo mat with a long side facing you. With dampened hands spread 1/2 cup prepared sushi rice onto mat, leaving a 1-inch border along the top edge. Spread a small bit of the wasabi paste horizontally across the center of the rice. Arrange 3 avocado slices and 3 cucumber slices, overlapping slightly in a horizontal line, over the wasabi paste and top them with one-sixth of the crab meat. Grasp the edges of the nori and the mat from the side facing you, lift the nori and the mat slightly, and roll the nori evenly and tightly away from you, pressing down slightly with each quarter turn. Seal the roll with a drop of water on the far edge of the nori, press the seam closed and transfer the roll to a cutting board. Make 5 more rolls in the same manner. With a serrated knife dipped in hot water trim the ends of the rolls and cut each roll crosswise into six 1-inch sections.