Mix mayonnaise, basil, lemon juice, garlic, garlic powder, and lemon zest together in a bowl. Season with salt and pepper. Cover with plastic wrap and refrigerate aioli until ready to use.
Preheat oven to 375 degrees F (190 degrees C). Place a wire rack inside a baking sheet to catch grease.
Place 3 bacon halves side by side on the wire rack. Weave another 3 to 4 bacon halves over and under those halves to form a square lattice. Repeat with remaining bacon halves.
Bake in the preheated oven until browned and crispy, 15 to 20 minutes. Lift bacon lattices off the pan with a spatula onto paper towels.
Spread basil garlic aioli on each ciabatta roll; layer mozzarella slices, tomato, and bacon lattices on top.
