Only a tiny minority of about 25% of the whole Lebanese population are actually of true/direct Phoenician ancestry. The rest are a wide mixture of Arabs/ Turks / Armenians / Greeks /Cyprians / Africans and so on.
There are also indigenous Phoenician communities found all over the Mediterranean coast. In Tunisia, Morocco, Algeria, Syria, Turkey, Malta, Italy, Algeria so on.
So really the concept of all Lebanese coming from Phoenicians bloodline is Scientifically a complete myth.
Not all Lebanese are Phoenician only a small percentage of them are. Lebanon is a mixture of cultures and a land where many empires have left their mark.
Source :
http://www.brightsurf.com/news/headlines
http://www.youtube.com/watch?v=IoPGLFY1L
http://phoenicia.org/genetics.html
http://wwwlb.aub.edu.lb/~webbultn/v6n6/i