Roasting mellows the garlic, and lemon brightens the taste of this sauce.
Preheat oven to 325 degrees. Top garlic with oil, zest, thyme, salt, and pepper, and wrap in parchment-lined foil. Bake until garlic is golden and soft, 1 1/2 hours. Unwrap, and let cool for 10 minutes. Squeeze garlic from peels, and puree with zest, thyme, and lemon juice in a food processor.
Combine garlic mixture and barbecue sauce in a medium saucepan over medium heat. Gently simmer for 5 minutes. Let cool, and refrigerate.