Heat grill to medium-low. Bring a large pot of salted water to a boil, and prepare a large bowl of ice water. In another large bowl, combine 2 tablespoons oil, garlic, lemon zest and juice; set aside.
Cook green beans in boiling water until crisp-tender, 2 to 3 minutes. Using a slotted spoon, transfer immediately to ice-water bath. Drain beans well, pat dry, and add to bowl with dressing. Set aside.
Toss onion wedges with remaining tablespoon oil; season with salt and pepper. Grill until lightly charred, 4 to 6 minutes per side. When cool, trim root end off, and thinly slice onions; add to bowl with green beans, and toss to combine.
To store, refrigerate up to 2 days.