Trim fat from meat. Place meat in a plastic bag, set in a shallow dish.
For marinade, in a blender container or food processor bowl combine coconut milk, lemongrass or lemon peel, lime juice, fish sauce or soy sauce, red curry paste, and sugar.
Cover, and blend or process until smooth.
Pour marinade over meat.
Close bag, and refrigerate for 4-24 hrs., turning bag occasionally.
Drain steaks, reserving marinade.
Grill steaks on the grill rack of an uncovered grill directly over med-hot coals for 12-15 mins., or to desired doneness (160 degrees F for medium doneness), turning once and brushing once with reserved marinade halfway through.
Discard any remaining marinade.
Remove steak from grill, and let stand 5 minutes
Thinly slice meat across the grain.
You can make marinade up to 24 hours ahead. Marinate steak as directed.