Disclaimer: I have played once and it was as baratheon. I am not intimately familiar with each card but believe I have a grasp.
It has been clearly stated that lannister can not hold riverrun in the first turn against a determined greyjoy, and jhagen has posted the "surefire" strategy to always win riverrun first turn and destroy lannister.
Using Jhagen's script, the greyjoy has placed march - 1 on his ship and march - 0 on pike.
Meanwhile, lannister placed march - 1 on stoney sept, support +1 on golden sound, and march +1 on lannisport.
Please remember: Lannister acts first on the first turn and may play 3 * order tokens.
Order of events in action phase:
Lannister resolves the march -1 to move the footman into lannisport.
Greyjoy resolves march +0 to move knight into riverrun and footman into seagard.
Lannister resolves march +1 into riverrun with 1 knight and 2 footman. (4+1 = 5 strength). support +1 is added from golden sound (now 7 strength). Kevan lannister is used (I am not sure if he is 2 or 3 or 4 strength but its irrelevant). Kevan adds 2 more strength for the footmen (9 strength) and lets say 2 for himself (11 str).
So greyjoy has played damphair and may pay 2 power to switch him out for... balon greyjoy? balon would increase the knights strength to 4 total and reduce lannister strength to 9. Euron would increase greyjoy strength to 6 but leave lannister at 11. Even if greyjoy had marched both the footman AND the knight into riverrrun this would be insufficient to withstand the lannister attack.
Actually, the support isnt even required in golden sound. You can play a defense + 2 in golden sound. That way when greyjoy attacks golden sound he is starting at -1 to your +2 and he no longer has aeron damphair so might have to blow balon or euron.
Anyway, if someone can tell me where I am wrong, feel free. Sure, its a lot of effort to win riverrun but thats a stronghold for you and 1 less for greyjoy.
Also, dont forget lannister has the raven and can switch out one of those orders if he sees something different shape up. Finally, the lannister player should be making every overture to stark to take advantage of a preoccupied greyjoy and start moving in from the north.