My 2 cents.......... Hopefully Soundofrockets will chime in - he's tried a bunch of amps with his LS9's. I've heard a couple of them and formed my own opinions, but they were relatively short listening periods - just a couple of hours with them. I will say that the Amps he had both sounded very good, but different. 1 SS, 1 Tube.
First of all, I have LS6's, so not the same speaker. They have a lot in common until you hit the bottom octave or 2. However, it's those bottom octaves that can place a lot of stress on an amp, so take it with a big grain of salt.
I'll start by saying what DIDN't work well with them - Emotiva XPA-1's and a Classe CAV-150 (multi channel HT Amp). Both had plenty of power and drove them well. They had decent tone and balance. However they were a bit short on Imaging - especially regarding the depth of the soundstage. I have also tried a small Class D amp (Folsom Chip amp) that sounds better, but just doesn't have enough power. to drive them in a large space. It sounds much better driving the Super 7's top end.
I bought a pair of used Odyssey Kismet mono blocks in Khartago cases with several upgrades. I only tried it with the LS6's for a short period of time, but long enough to know that they outperformed the other Amps by a considerable margin. I now use them with the Super 7's and am pretty happy. I am a bit behind on the latest upgrades, but I'm told that they are even better now. Great Amps!