I realize this is a huge topic. But given the stability and prosperity, especially in and around Beirut, during the 1950s and 1960s, how did religious tensions lead to civil conflict?
I advise you to read "A history of the modern middle east" by Cleveland and Bunton (2013). The answer to this question is multifaceted, as the origins of civil war are rooted in the make up of the postcolonial "confessional" Lebanese state, international relations, and a long series of internal and international historical/social/political developments.
The book explains this question extensively and is a good read.