Haha, good answer Ser Hodor. Part of what you said is why I disagree with zizzeus. There is a HUGE difference between 2 players teaming up to destroy you and one guy (or gal ) deciding to screw you. It gets much more complicated and harder to coordinate an assault by two players than having one player hammer another one out.

If you take a look at the other 4 houses, you have options to work with:
1. Stark can’t really be teamed up against. 2 players can attack him, but not in a coordinated manner.
2. Martell can usually find an alliance with either Tyrell or Baratheon. The fact that they have big deterrents in their house cards and map position also helps and makes the other two neighbours more willing to accept their alliance offers. Imagine if Lannister had Doran as a house card . And Even if both tyrell and bara team up against him, martell can turtle pretty hard.
3. Greyjoy doesn’t need discussing I believe.
4. Baratheon has interactions with 4 of the other 5 houses, I think you can find an ally or two in most situations. Last three games with Baratheon I’ve had 2-player alliances against me and I did just fine ... not because I can 1v2 like a boss but because Baratheon has options in their choice of allies.

Even Tyrell has options in my opinion, and the rose has more of a chance to recover after a rocky start. You need like the first 3 rounds with no mustering and first 2 rounds without a clash to be completely screwed against an aggressive martell.

With Lannister, it’s pretty much GJ alliance or bust. That’s not a matter of me not being able to see the intricate nuances of this wonderful game (although I am sure I am still ignorant on many details and subtleties the game has to offer). A binary choice made by one other player in the game can seal your fate, and that leaves little room for maneuvering. I’m definitely not asking for all houses to be perfectly balanced or identical, God no! I do wish that Lannister had an out once GJ decides to hammer you at the start. I know of only one such out for the Lannister player so far ... hope the GJ opponent plays like a potato

Bara is the most likely to get double-teamed, but I think his ability to weather it is less tied to the availability of allies than their unraidable sea support (which Lanni lacks), and ability to muster ships to fill it without help from the West cards (which Tyrell lacks).

I also think that Lanni is not as hopeless as all that in a GJ war. I've managed to slay the Kraken a handful of times, and the only thing that is remotely as satisfying in the entire game is shooting the moon with Tyrell and pulling off a multiple-Loras turn to just run riot across half the map.  It's why I like playing those houses the most right now, although I have by far the worst results with them.

But just because Lanni has a shot against GJ mano-a-mano does not mean the combat is equal. Lanni needs friendly-ish West cards and at the very least, no interference from Tyrell or Bara to manage it, and even then there is absolutely no margin for error.  Whereas Greyjoy should be able to roll with most West card combos, and can make a few slip ups that will simply delay their progress rather than cripple them permanently.  Lannister needs a little luck and a perfect deployment of Gregor/Cersei/Tyrion to wipe out their opponent. Greyjoy just needs Stark and Tyrell to keep to themselves (which as the late blooming-est houses, they generally will) while they keep hammering away. In a game with so many variables, the strategy with less moving parts to manage is going to carry the day more often than not.