Here's a recipe I found for traditional gyro meat. Doesn't look like any added carbs.
A traditional gyro should be made with at least 50% ground lamb, and the rest beef. The best ground to use is one with a high fat content (this is so that during the remixing it binds and keeps it shape well!). The main flavouring ingredients should always be: garlic, onion, marjoram, rosemary, salt and black pepper. Marjoram and Rosemary are similar to oregano and thyme in flavour (respectively), and are common ingredients in Greek cooking. True Greek food rarely uses oregano. The mass-produced Gyros use oregano, not to mention garlic and onion powder, but we used fresh minced garlic and onions. Here is the recipe we used where I used to work (compliments of Feller's Meat in Clearfield, Utah!)
1 lb. ground lamb
1/2 C. very finely chopped (or shredded) onion
2 tsp. fresh minced garlic
3/4 tsp. salt (preferably sea salt)
1/2 tsp. dried ground marjoram
1/2 tsp. dried ground rosemary
1/4 tsp. black pepper
Mix everything together and let sit in the fridge for 1-2 hours.
Blend in a food processor for about 1 minute. (When cooked, this will help give it a more traditional gyro feel on your palate. Otherwise, it just takes like cooked minced meat.)
Form into an oblong around a spit, and slow cook over a grill for around 30-45 minutes, cooking far from the coals, and rotating slowly. Alternatively, bake in the oven in a meatloaf shape for about 45 minutes to 1 hour, at 325ºF. It should be a bit dry.