This is a really fast dish to make, i have added a few different things to it but for the most part it is traditional. I never use to like this dish because sometimes the meat would come out dry but by adding more onions to it it stays nice and moist. This is how i make lahmeh bisayniyeh:
I start off with 1 pound of ground (lean about 10%fat) beef in a bowl.
I grate the onion (and cry a lot) with the course grate (not the really big one but not the small one)
About one medium/smallish onion is good for about a pound of beef.
Add in the onion and spices (some people add oil but i don't because i feel like it just all comes out anyways and then the outside is greasy)
Mix it really well
In any size pan pat it down with your hands so it is flat. I wouldn't make it too thin because when meat cooks it shrinks up so it will become thicker (plus i don't like thick pieces of meat)
Peel a potato (Typically there is no potato) you can use any type of potato but this one is typically used in Syrian cooking (usually you see the dark brown skinned one used more here in America.)
Arrange the tomato and potato slices nicely (make sure the potato is sliced thinly and the tomato is slightly thicker). In Syrian usually they just put tomato on top. Sprinkle with salt.
Cook it in the oven until the potatoes are cooked all the way through. Don't worry about the meat getting dry in the oven because it is protected by the tomatoes and potatoes on top and all the juice from the meat, onions and tomatoes will be released and it will surround the meat.
I like to eat lahmeh bisayniyeh with bread and yogurt and some fatoush but you could make msabaha (hummus) or any other type of dipping sauces like mhammara (roasted red pepper dip) or mtabbal (smoked eggplant dip)
1 pound of lean ground beef
1 medium onion
Sprinkle of salt and pepper
1 teaspoon of Arabic 7 spices