Preheat the oven to 400 degrees F. Cut the top off of the garlic, place on a piece of foil and lightly cover with the olive oil. Wrap entirely in aluminum foil and roast until the cloves are soft, about 40 minutes. Push the cloves out of the skins and smash into a paste; you should have roughly 1 1/2 tablespoons.
Whisk together the garlic paste, orange juice, ketchup, lime juice, sugar, chili powder, mustard, oregano, salt, ginger, black pepper, cayenne and lemongrass in a medium saucepan, bring to a simmer over medium heat and simmer until the mixture thickens slightly and darkens in color, about 20 minutes. Use immediately, or refrigerate in a nonreactive container for up to 2 days.
Cook's Note: The combination of orange and lime juices in the sauce makes a good substitute for the tangier taste of sour oranges, a traditional Cuban ingredient that's not always easy to find.