To make the sauce, stir yogurt, water and garlic together in a small bowl. Set aside.
Cover bread with water in a small bowl and let soak for 30 minutes.
Meanwhile, prepare a charcoal or gas grill: If using a charcoal grill, open vents in bottom of grill, then light charcoal. Fire is hot when you can hold your hand 5 inches above rack for just 1 to 2 seconds. If using a gas grill, preheat on high, covered, for 10 minutes, then reduce heat to moderately high.
Squeeze bread to remove as much moisture as possible. Put in a large bowl, add remaining ingredients, and mix with your hands until thoroughly blended. Divide lamb mixture into 16 portions and form each into a ball. Roll each ball into a 7- to 8-inch-long cigar, rolling it first between your hands and then on a work surface (be sure the kofte are uniformly thin for even cooking.) Slide a skewer lengthwise through center of each kofte.
Oil grill rack and grill kofte, turning once, until golden and just cooked through, 4 to 6 minutes. Let stand for 5 minutes, loosely covered with foil, and serve warm with yogurt sauce, wrapping them in lettuce leaves, if using.