In poker, players will often say the profit flows to the left. There is an objective advantage playing 'in position' which essentially means you see what your opinion is going to do, and react to it.
In AGOT, there is a similar advantage you can abuse and is probably one of the more effective ways of dealing with a war with GJ which is very rarely talked about especially in the early stages of the game.
In the first turn, GJ has a distinct advantage of being able to play 4 order tokens on the board during the first turn. They can do basically a few things... either attack goldensound and move onto land, or purely move their land troops using two march tokens.
Usually Lannister would ideally like to see what GJ is doing, if thats taking RR and seagard, or if they are leaving you to take RR.
Lannisters in order to gain maximum flexibility should always place a CP* on LP turn 1, and a march +1 on SS and a defense +2 on the golden sound. When you have the chance to use the raven you can decide if you would like to take a stab at riverrun (if GJ isn't attacking your ship, but is instead supporting or raiding) or if you're going to just accept that GJ has RR this turn.
So we can either march our FM to RR (perhaps with a support +1 form the GS if you have the chance) this would give you a 3 base strength and you can try bait out a card (the only thing is you must most likely use the hound which is pretty much a waste) or you can just straight up march... to the searoad marches.
This is probably one of the most important areas other than the stoney sept early on and is usually completely ignored.
SM is soo important because we know that GJ will always take RR (which contains a barrel and 2MP plus a PT) plus it can also attack RR so long as we hold the golden sound. If we can't have RR, the next best thing is searoad due to still potentially being on 3 supply if no muster comes, as well as having the ability to Kite GJ around on the next turn and use multiple marches to get an advantage.
So, it doesn't really matter what GJ does in this situation, but we will currently have a KN + FM in LP and a FM on searoad.
With the CP*, we should put 1 ship in GS and upgrade the FM to a siege engine.
The only thing Lannister should fear as this point is if GJ places march orders on either his FM or KN that aren't in RR to mount a counter attack with balon to lose a siege engine or if GJ goes for a sea assault and forces you back into the sound or worse, your port.
We can combat this, by using the fact we can place more marches as well as acting first. Usually you will place a march + 1 on LP and a march +0 on your FM in searoad, then we can place a march -1 on the ships.
The goal is simple, where possible we are trying to Cersei GJ with our forces in LP (we have a +7 strength, this will be possible if GJ is marching on sea (we can change to a support +1 which will be 9 to probably 4 max strength)
If this is not possible, then it might be a good idea to simply use clegane depending on how many troops are in RR or if its GJ's KN, because this is definitely worth it. (you could use march +1 on searoad instead of +0 and then change your march +0 to a +1 so you can change your +0 on LP to a support if you have the chance using the raven to give you 9 total strength.
Now the real reason we have a FM on searoad is because it gives us great counterplay to GJ having ship dominance over you at the start. If you suspect GJ is attacking you in the sound turn 2 (maybe they moved their ship from the port to ironmans bay t1) we can actually put a ship into the port rather than the golden sound. This means with a support + 1 in port and a defense + 2 on golden sound we can muster a strength of 5, which is a big deal. It means if you hold tywin lannister, the only way GJ can take your sea is if they use balon and they must use both ships. This means we can retreat to the sunset sea, which gives us access to... flints finger. A huge deal. If GJ goes for GS all in... you should move your troops to searoad, then if they take the sound with balon you can take flints finger (this means you will have ships in ironmans bay next turn if a muster comes up + you can muster ships in your port meaning you will basically have sea dominance and access to pyke with a siege ready and waiting to strike.
In practice, I have used this strategy to great effect, I actually could have taken pyke turn 3 had I gambled and played cersei on an earlier attack (he could still play euron and only euron to win) but for some reason GJ didn't. Anyway it meant I had to wait a turn to take pyke, but I cleaned up GJ the next couple of turns and took 7 castles a couple turns later.
Your Turn 2 strategy doesn't mention what happened in the Westeros phase... If there was a Mustering, Greyjoy had 6 mustering points to Lannister's 2, and if there was a Clash of Kings, Greyjoy had 6 or 7 PTs, while Lannister had 5 (assuming you had not left a PT in Stoney Sept).
Your whole strategy is assuming that all the units on the board are still the same as at the end of Round 1, and that you have three March orders while Greyjoy has two, neither of which is guaranteed.
1) A mustering / CoK comes up in round 2 and Greyjoy can easily consolidate his position
2) Greyjoy should not attack in round 2 without a mustering and instead focus on not losing Riverrun or the seas
I'd take the mustering point from Harrenal over the barrel of Searoad Marches
Add to it this little play from Tyrell...
Loras Tyrell can lead a march from Highgarden through Searoad Marches and into Lannisport.
I've actually seen Tyrell in Lannisport in Round 1 with Lannister putting a single footman in Searoad Marches early on.
Fear the Rose... They are growing strong!