Place the bacon strips in a skillet set over medium heat. Cook them until they become crisp and evenly browned.
Transfer the cooked bacon to a plate lined with paper towels so the excess grease can drain. Once cool enough to handle, crumble or break the bacon into pieces.
While the bacon cooks, arrange the thin tomato slices in a wide dish. Drizzle them with the olive oil and red wine vinegar, then season with salt and freshly ground black pepper.
Turn the tomato slices gently in the dish so both sides are lightly coated in the marinade. Allow the tomatoes to absorb the mixture while the remaining components are prepared.
Spoon the mayonnaise into a small bowl. Add 1 tablespoon of the tomato marinade, including the oil, vinegar, and tomato juices.
Stir the mayonnaise and marinade together until the sauce is smooth and fully blended.
Lay one low-carb wrap flat on a plate or clean work surface. Spread 1 tablespoon of the flavored mayonnaise evenly over the surface.
Add a portion of shredded lettuce, followed by 3 crisp bacon strips and 3 marinated tomato slices.
Roll the wrap firmly, keeping the filling tucked inside as it closes. Repeat the same process with the remaining wraps and filling.
Slice each wrap in half if preferred, then serve immediately.