I’m sure part of this calculation is the fact that Hezbollah is so reliant of Assad that they have been fighting alongside his troops in Syria for over a year now.
I think it's more the fact that Syria has 4x Lebanon's population, and a victory for the Sunni Arabs there means that Sunnis will also dominate Lebanon, where they are already close to numerical parity with the Shiites. Numerically-speaking there are 5x as many Sunni Arabs in Syria as there are Shiites in all of Lebanon. For Shiites in Lebanon, this is also an existential war, given Syria's traditional claim to all of Lebanon.