Hezbollah isn’t exactly a militia looking for a cause. They got their start resisting the early 1980’s Israeli occupation, and while they’ve had political and social work auxiliaries, the combat force has centered on fighting Israel.
Small deployments into Syria have been going on for awhile, but recently Hezbollah has been in direct combat more and more, with reports of 28 Hezbollah fighters killed in the ongoing fighting over Qusayr.
That has created some controversy in Lebanon, where the group’s supporters are concerned that their role in Syria risks more spillover violence, and is undermining their role as a hedge against Israeli invasion.
The US is also expressing “concern” about Hezbollah’s role, though that is likely more an excuse to condemn Assad, while Lebanese officials note that they can’t really force Hezbollah to not fight in Syria.