Heat gas grill to medium or prepare charcoal grill with medium-hot coals.
Cut a slit lengthwise in each hot dog, being careful not to cut through to other side. Cut each slice of cheese into 4 equal strips. Fold 1 strip lengthwise in half. Fit into sliced opening of one hot dog, pressing so cheese is not exposed past cut edge. Repeat with remaining hot dogs and cheese.
Place a strip of turkey bacon on a work surface. Diagonally wrap bacon slice around hot dog, enclosing completely. Snip a toothpick in half and use to secure both ends of bacon to hot dog. Repeat with remaining hot dogs and bacon.
Grill hot dogs 8 minutes, turning occasionally to cook on all sides. Be careful not to burn the bacon.
Split rolls, and spread one cut side of each roll with 1 tablespoon tomato-bacon mayonnaise. Top with 1/4-cup shredded lettuce. Remove toothpicks and place a hot dog on each bun.