Whisk together 1 cup of vegetable oil, 1/2 cups of vinegar, 2 cloves minced garlic, 1 tablespoon salt, and black pepper in a bowl; pour into a resealable plastic bag. Add the trimmed lamb leg, coat with the marinade, squeeze out excess air, and seal the bag. Marinate at room temperature for 2 hours.
Meanwhile, stir together the water, lemon juice, 3/4 cup of vegetable oil, tomato puree, onion, 2 tablespoons of vinegar, hot sauce, minced chile, 2 cloves minced garlic, mustard powder, and 1 teaspoon of salt in a large saucepan. Bring to a boil over medium-high heat, then reduce heat to medium-low, and simmer 30 minutes until the onions have softened and the sauce has thickened.
Preheat an outdoor grill for medium-low heat, and lightly oil grate.
Remove lamb from marinade, and shake off excess. Discard remaining marinade. Cook on the preheated grill 1 1/2 to 2 hours, turning and basting frequently with the hot barbeque sauce.