Pickle cucumbers: Halve cucumber (peel, if desired), then thinly slice crosswise into half-moons. Pick and coarsely chop mint leaves, discarding stems. In a medium bowl, toss to combine cucumbers, half of the chopped mint, 1 tablespoon vinegar and a pinch each of salt and sugar. Let marinate until ready to serve.
Prep ingredients: Finely chop 1 teaspoon garlic. Rinse and gently pat dry 6 lettuce leaves; wrap in a damp towel until step 6. Finely chop half of the onion (save rest for own use). Finely chop 1 teaspoon of the serrano pepper (save rest).
Prep sauce: In a small bowl, whisk to combine tamari, ¼ cup water, 2 teaspoons vinegar, and ¼ teaspoon sugar. Reserve for step 5.
Sauté turkey: Heat 1 tablespoon oil in a medium skillet over medium-high. Add chopped onions, chopped garlic, and serrano pepper; cook, stirring, until fragrant and onions are slightly softened, about 1 minute. Add turkey to skillet; cook, stirring occasionally and breaking up turkey into smaller pieces, until browned and cooked through, about 3 minutes.
Finish turkey: Add reserved tamari mixture to skillet, stirring to coat turkey. Bring to a boil, then remove from heat. Season to taste with salt.
Assemble & serve: Cut lime into wedges. Put lettuce cups on plates. Fill with turkey, then top with remaining chopped mint. Serve turkey lettuce cups with pickled cucumbers alongside, and lime wedges, for squeezing over top.