Marinate the ducks for 1/2 hour in a mixture of 1/4 cup oil and lime juice.
Rub ducks with the cut surface of garlic clove.
Place birds in a Dutch oven and cover with water; add carrot, leek, salt, and pepper and bring to a boil.
Simmer covered over low heat until birds are tender.
Remove birds from broth and cool.
Reserve 1/4 cup broth; store remaining broth for future use.
Remove the meat from the carcasses, cutting the breast meat into long, even strips.
Mix port wine, bay leaves, onion, pepper, and thyme; marinate the breast meat for 1/2 hour.
Set aside remaining duck meat.
Heat 3 tablespoons oil and butter in a medium skillet Saute duck'livers and beef liver over high heat until golden.
Warm fhe rum, ignite it, and pour it, still flaming, over the livers.
Stir in 1/4 cup of the reserved broth to deglaze the skillet.
Puree in an electric blender the liver mixture, reserved duck meat, and egg.
Coat heavily with lard 1 large terrine or loaf dish, or 2 small terrines or loaf dishes.
Put in half the pureed mixture, then arrange the marinated strips of duck breast on top with slices of truffles, if desired.
Cover with the remaining duck mixture, then with a thick coat of lard.
Garnish with bay leaves and green hot peppers.
Cover ter rine and place in a pan of hot water.
Bake at 375°F about1 1/2 hours.
Wipe clean the sides of the terrine.
Cool and store covered in refrigerator up to a week.
To serve, remove bay leaves and peppers; slice pate and accompany with salad.