Whisk together first 4 ingredients. Whisk in 1/3 cup olive oil until blended. Set aside.
Mince fennel fronds to measure 1/4 cup. Set aside.
Trim stalks from fennel. Cut fennel bulbs in half vertically, discarding cores. Cut each half into 1/4-inch lengthwise slices. Peel onions, and cut in half lengthwise. Cut each half into 1/4-inch lengthwise slices.
Combine fennel and onion in a large bowl. Drizzle 2 tablespoons olive oil over vegetables; toss well. Place fennel mixture in a grill basket. Grill, covered, over medium-high heat (350º to 400º) 13 minutes or until crisp-tender, turning after 6 minutes.
Add vegetables and fennel fronds to lemon juice mixture; toss well.
Tip: Use a grill basket with small openings to keep vegetable slices from falling through the grill rack.