Heat grill to medium-high. Once it is hot, clean the grill grate with a wire brush. Just before grilling, oil the grill grate.
Mix together the mayonnaise, tahini, 2 teaspoons of the lemon juice, 1 tablespoon water, and ¼ teaspoon pepper in a small bowl.
Mix together the fennel, oil, remaining tablespoon of lemon juice, and ¼ teaspoon each salt and pepper in a medium bowl.
In a separate medium bowl, gently mix together the lamb, coriander, cumin, garlic, ½ teaspoon salt, and ¼ teaspoon pepper with your hands until just combined. Form the lamb mixture into four ¾-inch-thick patties. Use your fingers to make a shallow well in the top of each patty (this will prevent overplumping during cooking).
Grill the burgers until an instant-read thermometer inserted in the center registers 140° F, 6 to 8 minutes per side for medium-rare.* Grill the buns, split-side down, until toasted, 10 to 20 seconds.
Stack the lettuce, burgers, slaw, and tahini dressing between the buns.
*This recipe includes the Real Simple test kitchen’s preferred cooking temperatures (considered safe by many experts) for burgers cooked to their juicy best. For maximum food safety, the U.S. Department of Agriculture recommends temperatures of 165° F for poultry, 145° F for fish, and 160° F for ground beef, lamb, and pork.