If the Lascarids actually attack the empire, this is what’s gonna happen. Many of the Greeks probably wouldn’t resist. They would just throw down their arms.They are just exchanging one emperor for another like god knows how many times. Trying their utmost, the Palaiologos government can probably just summon a few thousand soldiers at most, probably less because every knows that they are gonna lose.They will likely have to offer land to the Turks and the Serbs to get an army to help them fight, which would make them look like traitors.Civil war means being part of the same realm, which even though Constantinople might like to think as much about their vague link with Syracuse is not; Lascarids attacking the ERE would be an invasion. When they seized Byzantine Morea, it was in self defense against the unpopular act of an unpopular emperor.
Besides, I would not underestimate how important the shared sense of Greek identity was. In many ways, it was that sense that enabled the Lascarid conquest of Hellas from its Frankish overlords, that convinced many in Imperial Morea to either ignore or freely interpret Andronikos II's order so to help Ioannis' conquest of Achaea.
Unless the ERE attack the Lascarids first, is ruled by an emperor or a faction hostile to them, I don't see any Lascarid aristocrat pushing for it.
If anything, Angevin Sicily and Greece (it's my understanding they currently control something like Corfu, Aetolia, Locris and Arcanania) make more tempting targets than the ERE in the immediate.
Liberating fellow Greeks of the old Nicean homeland from Turkish rule however? That's more appealing and more unifying. Add to that more practical consideration as suppressing Turkish piracy, and you don't need much incentive to push some over the edge.
As for liberating Greeks from the Turks? That’s a poor idea if the Lascarids cannot conquer the rest of Palaiologian Greece. They’d be completely overstretched holding a few outposts across the Mediterranean.