Whisk together the oil, lemon juice, rosemary and garlic in a medium bowl to form a dressing. Season with salt and pepper to taste.
Place the potatoes in a medium bowl; add 2 tablespoons of the dressing and toss to coat.
Place the turkey in a separate medium bowl; add 2 tablespoons of the dressing and toss to coat. Let the potatoes and turkey marinate at room temperature, turning them occasionally, for 15 to 30 minutes.
Preheat grill to 350-degrees.
Remove the turkey cutlets and potatoes from the marinade and transfer to separate rimmed baking sheets; season with salt and pepper.
Grill, turning them once, until they are charred and cooked through. The turkey should cook for 4 minutes per side, or until a thermometer registers 165 degrees.
Grill the potatoes for about 10 minutes per side. Put the turkey and potatoes on plates and drizzle on remaining dressing.
Serve warm.