I don't believe there's a big cultural gap between Lebanese Christians and Muslims.
Most urbanized Lebanese youth are shunning old traditions and adopting a more Western lifestyle, whether they're Christian or Muslim.
If you go to Mar Mikhael, you'd notice that half of the clientele is Muslim.
The cultural differences exist mainly between the Hizbullah community/Jame3a Islemiyyeh/Salafists and the rest of Lebanon.
That's why there's a perceived cultural divide between Muslims and Christians. But in truth, it's a divide between Christians/secular Sunnis/secular Shiites on one side and Shia and Sunni Islamists on the other side.
The cultural divide argument started emerging when Christian nationalists wanted to divide Lebanon based on what is recognized internationally as a nation. The Kulturnation in comparison with the Staatnation, are two concepts of nationalism that came out of Europe. The former was in Germany in response to the latter which emerged from the French Revolution. In the French concept, culture, race and language does not make the nation, but the territorial state defines the population and its identity.
The Germans on the other hand constructed nations based on "culture" and "cultural differences" to separate the German from the Jew. German nationalism takes biology, culture, and tribal roots as central to the idea of the nation.
Pierre Gemayel was the pioneer of constructing the concept of the cultural nation into the Lebanese Christian identity, something he admired in and learned from Nazi Germany.