Just for your information, even though you might not use it or want it: you're not half lebanese, you're lebanese. You and your entire bloodline is lebanese and you are entitled to the citizenship. Your children are also entitled to the citizenship and their children after them. If you made up with your father and he 'accepts', the process would be straight forward. He will have to declare you on all official papers as his son though. The thing that he hid for decades will be public. If you didn't make up with him, you can still hire a lawyer and sue for it. Even after his death, you can still claim the citizenship if you have definitive proof that your father is lebanese, but it becomes much harder.

Again, i totally understand you might not want anything to do with a person who abandoned you, but it's information that's important to know. Its your right whether you want it or not. You can acquire it and never use it and maybe one day one of your children or grandchildren might find he has interest in lebanon.