You could trace it back to the 1948 Arab-Israeli war. Lebanon supports the Arab states, the Palestinians spill into Lebanon, and fighting continues over various decades (50's, 70's, 80's, 90's), including a civil war that took 16 years, after which point it's sort of Syria, Israel and Hezbollah grappling through Lebanon, of course with the other usual cast of characters (US, UK, Iran, Saudi, and a dozen different rebel groups).
But probably the majority of the current crisis stems from the 2006 war.