Okay, now we can see the great complexity of your situation. Are you still in Lebanon?
I can only speak from my personal experiences in the US and from what I know of persons who lived in a few other countries such as Australia and Canada.
As a general rule, you would need to supply the following:
1) Proof that your grandmother was born an Italian citizen. You would have to determine exactly where and when she was born and then obtain a copy of her Italian birth certificate.
2) Proof that your grandmother was still an Italian citizen at the time of your father's birth. I have no idea how you would accomplish this; in the US, Canada, or Australia, we would request from the government documents which show when our ancestor became a naturalized citizen or a letter which certifies that no documents exist. You would need this proof from Egypt (where your father was born) and also from any other country your grandmother lived in after leaving Italy.
3) Your father's birth certificate from Egypt.
4) Proof that your father never renounced his right to Italian citizenship. If he is still living, he can attest to this in writing.
5) Your birth certificate from Lebanon.
This is a greatly simplified example of the requirements. If you are still in Lebanon, you should contact the Italian Embassy in Beirut (
http://www.ambbeirut.esteri.it/Ambasciata_Beirut ) and ask their advice.
Good luck!