I have played a few games as Mono Lannister. Although their core strategy is to destroy the opponent's hand, more often than not I found it was myself without any cards in hand. This tended to arise due to playing out the starting cards via my excess gold and then not being able to generate excess draw- resulting in a lot of excess gold in subsequent turns.
I think that for now it would be best to ally Lannister with another faction, primarily to bring in higher cost characters to spend the gold on, as well as additional draw. I was thinking to try Baratheon- just 3x Melisandre, 3x Fiery Followers, 3x Seen In Flames for kneel (1.0 throwback!), and Chamber of the Painted Table to combo with The Iron Throne for power. Other allies would be entirely possible, it just depends on your preference. I myself really like the red lady
I'm really looking forward to the chapter packs to strengthen mono Lannister though!
Comparing with the other Houses, it seems that the decks are not yet consistent enough to make a firm judgment. You may play the same game twice and experience entirely different outcomes due to the high draw variance. If certain Houses get certain key cards early then they can dominate.
On that note, I hope the trend will change but for now, there remains a high possibility of a very one-sided game (which was a problem in 1.0 too). This seems to be driven by limited draw options. Noting though that we only have the Core set right now- and bearing that in mind, FFG has certainly done a great job!