My grandmother was Lebanese. Many of these dishes are similar across the eastern Mediterranean, but god help you if you get it wrong!
Having a Greek heritage in my family sets up many possible intramural matches!
The first thing I would say is that it is hard to find the exact pita bread that my grandmother would accept. The only bakery I buy from is a local supply shipped from Montreal, so good luck! It is flatter and thinner than most you can find. She called it “Syrian” bread, which would have made sense since at the time she emigrated, Lebanon was part of Syria.
In any case, the iconic dishes are stuffed grape leaves - Warak Enab-(with pine nuts if you can find them!), Hummus (chickpea based), Kibbeh (bulger wheat+lamb), tahini (sesame spread), Taboulleh (salad, again bulgur wheat, lemon juice, olive oil, parsley, mint, etc.), Falafel, lebneh cheese (creamy mild cheese used as a spread) Baklawah (simple syrup, rose water walnuts, layered pastry). The Baklava most are familiar with is the Greek, which uses honey instead of the simple syrup) Baba Ghanoush is an puréed eggplant dish.
As you can see, these are the kind of dishes you would use as a selection for browsing and combining through a meal. Lots of salads with toasted Pita Breads.
Enjoy!