If you do not care for lamb meat, here are Instructions for making an Imitation looking Gyro that doesn't 
contains lamb meat, 
How to make a Gyro BURGER and  how to make a real Greek Asian Style Gyro Meat loaf that can be sliced thin.

Imitation (phony) Gyro Sandwich
Minute frozen steaks like Steak-um or Philly Steaks
will make a quick substitute for an authentic looking
gyro sandwich.

For the phony gyro, pan fry some Steak-um or Philly Steaks under a medium heat with ¼ cup water, 1/4 teaspoon Worcestershire sauce, pinch of salt, pepper and 1/8 teaspoon of garlic powder. As soon as the water boils away flip them over once and fry another minute or until no longer pink and starts to brown. Stuff some of the cooked meat, tomatoes, onions into the pocket of a 1/2 slice of pita bread or roll a whole soft pita bread up like in the photo. Add 1-tablespoon cucumber sauce click here for the Gyro cucumber sauce recipe and for those that have problems with dairy products, try this Lebanese Garlic sauce with Lemon and Olive Oil.

About making Sandwiches; Use sweet or mild onions, slice into thin slices and crush them with the bottom of a cup, let them set out to reach room temperature. The tomatoes should be sliced in thin wedges and they as well as the pita bread should be left out long enough to reach room temperature. The sauce should be cool from being refrigerated, only the meat should be warm.

Stuff the pocket of ½ of a pita bread with some cooked minute steak meat, tomatoes and onions and spoon in some sauce. If you want, you could also jelly roll everything up in a whole pita bread like in the photo shown above. Enjoy

Another type Sandwich that does use lamb meat is a GYRO BURGER sandwich:
Gyro Meat Burger Ingredients:
½ lb ground Lamb
½ lb ground Beef
1/2 teaspoon dried oregano, crushed
½ teaspoon garlic powder
½ teaspoon pepper
1/2 teaspoon onion powder
1/4 teaspoon ground cumin
1/2 teaspoon salt

Gyro Burger Instructions:
In large bowl, combine oregano, garlic powder, pepper, onion powder, cumin and salt, ground lamb and ground beef , mix well

Gyro Burger Cooking Instructions:
Form into 4 patties, about 3/4-inch thick. Grill over medium coals or broil about 5 minutes on each side to a desired degree of done.

Make the burger sandwich:
Using 2 pita bread rounds (6-inch), halved crosswise
Place gyro-burger in the pocket of a ½ slice of pita bread top with some chopped spinach, onions, tomatoes and cucumber sauce.
Makes 4 Gyro Burger Sandwiches

How to Make an Authentic Greek Gyro Loaf Recipe.
Gyro of Greece - Some Middle Eastern names for a gyro sandwich are Shawarma, Chawarma, Shuarma, Shawerma, Shoarma or Shaorma

Gyro Meat Ingredients:
2 lb fine-ground hamburger *high fat content at least 30-33% fat or higher or mix 1 lb ground meat and 1 lb fine-ground lamb
3/4 cup onion minced fine
4 minced clove garlic
2-1/2 teaspoons oregano
2 teaspoons salt
1 teaspoon black pepper
1 teaspoon marjoram
2 tablespoons crushed dry mint leaves

Gyro Meat Loaf Method:
Sprinkle everything all over meat
Before mixing it in with the meat, use disposable food handlers gloves; blend everything in a food processor for about 1 minute,
Thin with a few drops of water if needed. Hand-pat
Then squeeze very tightly into a compressed oval
Shape meatloaf then refrigerate overnight.

Next day, preheat oven to 350-F and bake
for 50-60 minutes until somewhat dry
(Some may prefer to cook the loaf in a rotisserie oven.)
After cooked; let loaf set and cool to just warm before slicing thin. To brown slices, pan-fry them under a medium heat with a small amount of extra virgin olive oil.

*Hamburger fat helps to bind loaf together so the more fat contents the better.

Makes about a 1-½ pound cooked loaf.

*Roll-up some thin sliced gyro meat, tomato wedges, thin sliced onions and a heaping tablespoon of sauce in a whole soft shell pita bread (see photo) or stuff the items into a 1/2 slice of a pita bread pocket and spoon in some sauce.

About Gyro:
Doner kebab is a Greek dish made of roasted meat cooked on a vertical spit. It is also known regionally as gyro or in some places pronounced yeer-oh, jy-roh, zheer-oh, shawarma and shepherd style. It consists of shaved lamb, goat, chicken, turkey, beef, or mixed meats roasted on a spit. Less common alternatives include fish and sausage. It is often served wrapped in a flatbread such as a pita or tortilla, and is a common fast food item in The Middle East, Europe, the Caucasus, North America and Australia.

In a prepared dish, seasoned meat is stacked on a vertical spit in the shape of an inverted cone. It is turned slowly, cooking against a vertical rotisserie. A tomato, onion or pineapple may be placed at the top of the stack for additional flavoring. The meat is cooked by charcoal, wood, cast iron, electric, or gas burner. If the meat is not fatty enough, strips of fat are added so that the roasting meat remains always moist and crisp. The rate of roasting can be adjusted by varying the strength of the heat and the distance between the heat and the meat, allowing the cook to adjust to varying rates of consumption. The outside of the meat is sliced vertically in thin, crisp shavings when done. While cooking, the meat is shaved off the stack with a large knife, an electric knife or a small circular saw, dropping to a circular tray below to be retrieved.

Toppings include tomato, onion, lettuce, lavash, tabbouleh, fattoush, eggplant, parsley, pickled gherkins, cabbage, pineapple, cucumber and pickled turnips. Sauces include tzatziki, tahini, hummus, amba, salsa, hot sauce, garlic mayonnaise, toum (garlic sauce), pomegranate concentrate, lime juice, skhug (a hot chili sauce), tahini-based tarator, Greek white cheese, or flavored with vinegar and spices such as cardamom, cinnamon, and nutmeg.