Place broccoli in a large bowl. Combine the lemon juice, oil, salt and pepper; drizzle over broccoli and toss to coat. Let stand for 30 minutes.
Toss broccoli, then drain marinade. Place cheese in a large resealable plastic bag. Add broccoli, a few pieces at a time, shake to coat.
Using long-handled tongs, moisten a paper towel with cooking oil and lightly coat the grill rack. Prepare grill for indirect heat using a drip pan. Place broccoli over drip pan and grill, covered, over indirect medium heat for 8-10 minutes on each side or until crisp-tender. If desired, garnish with shaved Parmesan and fresh basil.