Theodore Lascaris is defeated by the Seljuk/Latin coalition at the battle of Antioch on the Meander in 1211. Does this eventually mean a stronger Latin empire or does it mean that eventually the Greek despots of Epirus take the lead?
What's he doing at Antioch? *Quick Wiki search* Oh, you mean Antioch on the Meander. Two totally different places.
Well, interesting read. Well first, and this is according to the Wikipedia, there wasn't a "coalition," but simply the Turks fighting the 'Byzantines'. Indeed, the Byz had employed some Latin mercenaries, so there's your 'coalition' if you want one. Later on, however, the Latins moved to force Nicaea to give up land, but not at this particular battle.
The Seljuks were only assisting the exiled Emperor Alexios as an excuse to hit the Nicaeans. This won't change things. He *likely* won't be allowed to take over. At least not totally; he'll still be a client likely if allowed to rule at all. Of course, this could lead to the Seljuks using him
further by saying "We helped you here, now we'll help you there" and move to attack the Latin Empire.
Epirus will likely be the ones to jump saying they are now the rightful heirs of Byzantium, but I'm pretty sure everyone will see them as jokes. Trebizond is marginalized by the Turks, and Greece is splintered into various kingdoms and duchies. I suppose the Latins could actually make a play for it, saying they have 'brought Latin back to the Romans' or somesuch.
I don't know much of the history of this region, but the Seljuks later decline (though the Ottomans are still around to do something maybe) while the Nicaeans in OTL forced the Latins to decline. Hmm. I don't see either power making a real lasting impression, especially the Latins. The Seljuks will fall eventually into some other Turkic state or another (or a dozen) and the Latins will still be strangers in a strange land with naught but greedy eyes on their frontiers.