Light a grill. Arrange 3 of the grape leaves so they're overlapping; repeat with the remaining leaves. Cut off the red flesh from the underside of each fish fillet. Set the fish on the leaves and season with salt and pepper. Enclose the fish in the leaves and brush each fillet with 1/2 tablespoon of the oil.
In a bowl, whisk the lemon juice with the garlic, anchovy, herbs and 3 tablespoons of the olive oil; season with salt and pepper.
In a small bowl, toss the grapes with the onion and the remaining 2 tablespoons of olive oil. Season with salt and pepper. In a perforated grill pan, grill the grapes and onions until softened, 4 minutes; transfer to the lemon dressing and toss.
Grill the wrapped fish over high heat, turning once, until the fish is just cooked, 6 minutes. Serve with the onions and grapes.
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