Toss broccoli and lemon wedges in half the oil and salt and pepper.
Place broccoli in grilling basket; hold lemon. If cooking over open flame, line with foil to curtail flareups. Otherwise the broccoli can be placed directly on the grate to mark.
Cook for about 15 minutes, turning occasionally.
Add lemon to broccoli or place directly on grill for last 10 minutes.
Remove broccoli to serving dish; toss with remaining oil. Squeeze 2 lemon quarters over broccoli, tossing. Be mindful of seeds—they will be bitter if bitten into. If lemon is too hot, handle with paper towel. Reserve remaining lemon to squeeze over broccoli to individual taste. Be mindful of lemon seeds. Salt and pepper to taste.
Note: A variation would be to add ground garlic or garlic salt while tossing broccoli and lemon with oil. Do not use fresh garlic; it will overcook and turn bitter.