To cook the rice: Thoroughly rinse the rice. Transfer to a rice cooker with the water and cook using the rice setting for about 30 minutes. For the stovetop method, bring the rice and water to a boil, reduce the heat to low, cover, and simmer for 15 minutes. Turn off the heat and let sit, covered, for another 15 minutes. Fluff and keep warm.
To prepare the salmon: In a mixing bowl, whisk together the mayonnaise, Sriracha, and salt. Add the salmon and toss until evenly coated.
To assemble the sushi cups: Cut each roasted seaweed sheet in half and stack two halves together. Add about 1½ tablespoons of warm rice on top, then gently press the seaweed and rice into a standard-size muffin tin to form a cup. Repeat with the remaining ingredients, then spoon the salmon mixture over the rice.
To bake the sushi cups: Preheat the oven to 400°F (204°C). Bake on the middle rack for about 15 minutes, until the salmon is cooked through. Remove from the oven and let cool slightly.
To serve: Top each sushi cup with diced avocado and a squeeze of lemon or lime. Add extra Sriracha if desired and serve warm.