In large bowl, combine oil, lemon juice, chopped onion, thyme, garlic, salt and paprika.
Add lamb pieces; turn to coat with marinade.
Cover and refrigerate 6 to 8 hours or overnight, turning occasionally.
In saucepan, cook cauliflowerettes, carrot and white onions in boiling water to cover until tender-crisp.
Thread lamb and all vegetables alternately on skewers.
Grill kabobs, on uncovered grill, over medium-hot briquets 13 to 16 minutes, turning often and basting with marinade.