"I think it would be cool if there was something like a draco-lich in my game and I'm wondering what it could do to really drive conflicts both short-term and long-term,"
Not certain if you actually want ideas about this in particular, or if it was just a hypothetical, but it is fun to think about anyway.
In the short term, IDK where your game is set, but most ancient armies used a volunteer militia type of system, so theoretically he could cause a famine just by making the local cities keep their armies raised, due to there being no one to bring in the harvest or plant it on time depending on the season.
That's rather mundane by exalted standards though, so maybe the local lords have conscripted the gods of the fields in the hopes of contesting this monster, or maybe the dracolich has unleashed a plague upon the field gods specifically, leading to a blight with a non obvious cause.
Maybe the dracolich got into cahoots with the god of the local aquifer, convincing it to only use it's cleansing powers in exchange for prayer. The aquifer God doesn't know that any toxins in its aquifer will eventually be taken up by the plants and animals, because it isn't their department.
Maybe the Dracolich would rather not be at the top of everyone's minds, so it unleashed a hearteater to distract silver pact and sidereal troubleshooters who might otherwise take offense to it.
Does the dracolich know any martial arts? If it knows black claw style then it could try to make an immaculate heresy casting itself as a sixth Immaculate Dragon, with black claw posing as Death Dragon Style or whatever.
Do you want your dracolich to have influence in the underworld? Maybe it's assembling some ghosts that way, and the nearest deathlords march on their rival and only show up after the circle has killed it?
Going back to that immaculate heresy idea, the dracolich could probably pass off being possessed by a ghost for granting ira blessing like the immaculate dragons do to dragon blooded.