Bring first 5 ingredients to a boil in a small saucepan, stirring constantly. Cool completely. Reserve 1/3 cup mixture.
Place lamb and onion in a shallow dish or large heavy-duty zip-top plastic bag; pour remaining teriyaki mixture over lamb. Cover or seal, and chill 1 hour, turning occasionally.
Remove lamb and onion from marinade, discarding marinade.
Alternate lamb and onion on 4 (8-inch) skewers.
Coat food rack with cooking spray; place on grill over medium-high heat (350° to 400°). Place kabobs on rack, and grill, covered with grill lid, 8 minutes or to desired degree of doneness, turning and basting occasionally with reserved teriyaki mixture.