To make the tzitziki, cut the cucumbers in half lengthwise. Scoop out the seed pulp and grate the cucumber halves.
Press the grated cucumbers to remove excess water and mix with yogurt, garlic, olive oil, white vinegar, salt, and black pepper.
Marinate lamb shanks with olive oil, salt, pepper, and oregano for 2 hours. Preheat oven to 400°F and cook for 2.5 to 3 hours.
For ground lamb, heat onions in olive oil, add remaining ingredients, and cook until browned.
For the rice, boil water, rice, lemon juice, oregano, oil, and salt, then simmer for 12-15 minutes.
Assemble the burrito with guacamole, rice, lamb, tzitziki, queso fresco, tomato slices, and cayenne pepper.
