Heat gas grill to medium-high or coals in a charcoal grill to medium-hot. Lightly coat grill rack with oil or cooking spray.
Form the ground round into 12 equal-size patties. Grill for 2 minutes per side, covered, or until internal temperature registers 160 degrees F on an instant-read thermometer. Place cheese on top of each burger during last minute of cooking.
Spread cut side of each roll with 1 teaspoon relish. Top with slider, sliced tomato and lettuce. Serve immediately.