In a medium bowl, combine the cooked shrimp, mayonnaise, sriracha sauce, and lime juice. Mix well until the shrimp are evenly coated. Set aside.
Prepare your sushi rice according to package instructions, then let it cool to room temperature.
Using a round mold or a small cup, layer the ingredients starting with a spoonful of sushi rice at the bottom. Press down gently to form a base.
Add a layer of sliced avocado on top of the rice, followed by a layer of the spicy shrimp mixture.
Add another layer of sushi rice, pressing down gently again. Top with cucumber slices and a sprinkle of sesame seeds.
Carefully remove the mold or cup to reveal the stacked sushi. Repeat the process for the remaining ingredients.
Serve the sushi stacks with soy sauce on the side for dipping.