Combine the vinegar, 1 tablespoon olive oil, the mint and half of the garlic in a medium bowl; season with salt and pepper. Add the steak; let marinate 10 minutes.
Cook the bulgur as the label directs. Meanwhile, preheat a grill or grill pan to medium high. Make the tzatziki: Whisk the yogurt, grated cucumber, 1 tablespoon each water and olive oil and the remaining garlic in a small bowl; season with salt and pepper. Refrigerate until ready to serve.
Brush the grill grates with olive oil. Remove the steak from the marinade and pat dry. Grill the steak until well marked, 6 to 7 minutes. Flip and continue grilling until marked on the other side, 5 to 6 more minutes for medium rare. Transfer to a cutting board and let rest 5 minutes, then slice against the grain.
Fluff the bulgur with a fork and stir in the remaining 1 tablespoon olive oil, the sliced cucumber, tomatoes and parsley; season with salt and pepper. Divide the lettuce among plates and top with the bulgur mixture, steak and tzatziki.