Why would the Lannisters have anything to do with who succeeds Tommen? As far as the throne is concerned he's a Baratheon, wouldn't someone from that line be the king? Obviously the Lannisters will try to keep the throne but they have no claim, unless their are no Baratheon's left right?
Yeah it's going to come down to whoever has the biggest army in the city. Then they have to keep everyone else at bay.
The Tyrells are currently occupying KL, but I don't think they'll be able to put Loras on the throne with the Faith around.
In the end I think Dany shows up and is the catalyst for change in Kings Landing.