In a mixing bowl, combine lamb mince, oregano, garlic, salt, and pepper. Mix well and let it rest for 5 minutes.
Heat olive oil in a frying pan over medium heat. Add the lamb mixture, cooking for about 8-10 minutes until browned and cooked through. Stir occasionally to ensure even cooking.
Add the canned tomatoes and chopped basil to the pan with the cooked lamb. Stir well and simmer for an additional 5 minutes until the sauce thickens slightly.
Lay a whole wheat wrap on a flat surface. Spoon an even amount of the lamb mixture down the center, then top with grated carrots and cucumber slices.
Roll the wrap tightly, tucking in the sides as you go. Repeat for all wraps.
Place the wraps seam-side down in the frying pan for 2-3 minutes to lightly toast them. Remove and let rest for a few minutes before cutting in half.
Serve the wraps with a side salad and lemon wedges, if desired.
