I think this combination deserves it's own thread as it has many versions available to it. I have seen 4 deck lists for Lannister banner of the Rose and they're completely different. Of course certain key cards remain fairly consistent throughout. Lets explore all the themes available.
Tywin, Randyll, Jamie, KotF.
sitting with any 3 of these after a wildfire you're in a pretty strong position. Multiple renown is pretty scary on defense, your opponent often has 3 difficult choices, either passing the challenge phase, making chud challenges giving you easy power, or over-committing to attacks.
Lannister has access to 2 of the best control events going in TTIDFL and Treachery, throw in the Hands Judgement, Tears, Milk, the Bear to manipulate your opponents deck, Varys with bodyguards and duplicates,
Pretty good answer to unopposed stealth challenges, and messes with your opponents challenge maths. All except 1 are Lannister, the exception is the best ambush character of all Olenna's Informant who happens to be a Non-Loyal Tyrell card.
The Bear and the Tickler. Not much beats Bearing a Baron/Tywin/Rob to the top of your opponents deck, and then tickling it to death along with it's in-play copy.
TTIDFL and the Queens Assassin. Playing TTIDFL to remove your opponent's soul chud, and then hitting them with an Assassin can be game swinging. Difficult to pull off as you need both in hand, at least 6 gold, and the right opportunity, but maybe the best 2 card combo in the game when it works.
Left and Right. Some IMO undeserved stuff written about these 2. Not least the likelihood about keeping both of these during a Wildfire. Sure if you have 3 big hitters they can both go, as by then no doubt they've done a job, but what about if you have 2 big hitters say Tywin and Jamie or KotF. What's a 3 strength bicon that doesn't kneel to defend worth, easily 4 gold maybe 4.5. whereas a 2 strength monocon is barely worth 1.5. Killing both is equivalent to losing probably 8.5 gold worth of character killing just 1 is losing a hefty 7 gold worth of character. To me killing Jamie or KotF is an easy decision in those circumstances unless they are duped up and with power.
Super Randy T
The normal Tyrell package of Margaery, Heartsbane, and Growing Strong, throw in Widow's Wail, Little birds, bodyguards, treachery, seal of the hand the hand's judgement, and a suite of plots to support and you have a pretty heavy hitter you can use 3 or 4 times per turn who is difficult to stop.
Tywin, Littlefinger, Moneylenders, Tyrion can generate a whole bucket load of money to pay for your control events and/or ambush effects, or be able to swing dominance. A standing Tywin with say 6 gold, that's 18 for dominance to start with.
Got a lot better with Here to Serve. Having the ability to get either GM Pycelle or M Lomys is handy. Cersei, Casterly Rock and Olenna's Informant can pretty much strip an opponents hand in 1 turn. Add to that the fact that you can guarantee to ambush in Olenna's Informant if you have Tyrion in play.