Place strips of lamb in shallow dish. In bowl, combine soy sauce, brown sugar, oil, vinegar, garlic, sesame seeds, ginger and salt; reserve 1⁄4 cup marinade for basting.
Pour remaining marinade over lamb. Cover and refrigerate meat for 4 to 12 hours, turning occasionally. To assemble teriyaki sticks, remove meat from marinade and discard marinade.
Thread lamb strips on bamboo skewers accordion fashion alternately with water chestnuts, pineapple chunks and cherry tomatoes.
Grill over medium hot coals. Cook 4 inches above coals for 6 to 8 minutes or until desired degree of doneness, brushing occasionally with marinade. Turn teriyaki sticks frequently during cooking time. Serve immediately.