Preheat the oven to 400°F and line a baking sheet with tin foil.
Make the aioli: In a small bowl, combine mayonnaise, Greek yogurt, minced garlic, lemon juice, salt, and pepper. Mix well and set aside.
Assemble the bacon-wrapped Brussels sprouts: Cut 10 pieces of thick-cut bacon in half, making 20 pieces in total. Place a piece of bacon flat on the baking sheet, then put a Brussels sprout at the top and roll it up. Ensure the seam side is facing down on the baking sheet. Repeat for all.
Spread out the bacon-wrapped Brussels sprouts so they're not touching, then bake for 30-40 minutes, depending on how crispy you prefer your bacon.
Serve immediately with the prepared aioli.