Slice the tender portion of the green garlic thin and discard the tough stem ends. In a mortar and pestle, crush the sliced green garlic to puree, add the thyme leaves, the lemon peel, and olive oil and work into a paste. Add the juice and season with salt and pepper.
Slash the fish three times on both sides all the way to the bone and rub the marinade on the fish and season well. Grill over medium-low heat, turning half way through. Grilling time should take 15 to 20 minutes.