To prepare caviar, place seaweed in a large bowl; cover with hot water to 2 inches above seaweed. Cover and let stand 30 minutes or until soft. Drain. Rinse with cold water, and drain. Place seaweed in a food processor; process until minced.
Heat oils in a large nonstick skillet over medium heat. Add seaweed; cook 3 minutes, stirring occasionally. Add 2/3 cup water, soy sauce, and garlic; bring to a boil. Reduce heat; simmer 6 minutes or until liquid evaporates.
To prepare remaining ingredients, peel lemon, and cut lengthwise into 6 wedges. Cut each wedge crosswise into 8 pieces to yield 48 triangles.
Place 1 teaspoon seaweed caviar on each cracker. Place Lemon Tofu Cream in a small zip-top plastic bag; seal. Snip a small hole in 1 corner of bag; pipe about 1/2 teaspoon tofu cream on each cracker. Place 1 lemon triangle, 1 chive piece, and 1 carrot piece on each cracker.