Cut the avocado in half, remove the seeds and peel the flesh. Peel garlic and chop finely. Squeeze lime. Finely puree buttermilk, avocado, garlic and lime juice. Season to taste with salt, pepper and sugar.
Wash the meat, dab dry, cut into cubes and mix with half the marinade. Chill for about 1 hour.
Put the ingredients alternately on metal skewers or wooden skewers soaked for about 1 hour. Grill on the hot grill or in an oiled grill pan for approx. 6 minutes each while turning.
Serve the grilled skewers with the rest of the lime-avocado sauce.