Preheat the oven to 250 degrees F (120 degrees C).

Prepare duck: Place duck legs into a large bowl and drizzle with oil. Sprinkle with salt, five-spice powder, and black pepper; mix to evenly coat.

Sprinkle large green onion pieces into a baking dish large enough to hold duck legs in a single layer. Place duck legs, skin-side up, on top of green onions. Scatter garlic over duck. Place a piece of parchment paper directly on top of duck to help retain moisture. Cover the baking dish tightly with aluminum foil.

Bake in the preheated oven for 3 hours. Turn off the oven, crack open the oven door, and let duck rest in the oven for 1 hour; do not uncover the dish during this time.

Remove the dish from the oven and let cool to room temperature. Baste duck with rendered fat in the dish. Place the parchment paper back over duck and re-wrap the dish in aluminum foil. Refrigerate for 8 hours to overnight.

Make sauce: Mix together hoisin sauce, lemon juice, sesame oil, and hot sauce in a small bowl. Set aside.

Remove duck meat from bones; leave skin on. Cut meat into 1/2-inch cubes.

Remove 1 tablespoon rendered fat from the dish to a skillet over medium-high heat. Cook and stir 1/2 of the cubed meat in hot fat until pieces are brown and crispy, 4 to 5 minutes. Add remaining meat; cook and stir until duck is just heated through, about 1 minute more. Stir in 1 tablespoon chopped green onion.

Spoon duck mixture into lettuce leaves. Drizzle with sauce; garnish with cucumber, green onions, and sesame seeds.