Hidden below Lysandre Café in Magenta Plaza of Lumiose City is Lysandre Labs, the secret headquarters of Team Flare.
As soon as you go up the stairs, you meet Lysandre, and must battle him. Lysandre has a level 45 Mienfoo, a level 45 Murkrow, a level 47 Pyroar, and a level 49 Gyarados.
Explore the Lab
After you defeat Lysandre, he says you have to find the Elevator Key from one of the scientists.
The lab is full of warp tiles and direction arrows. If you step on a direction arrow, you are pushed in that direction until you bump into something.
The only way that you can go right now is to the left, using the upper left arrow tile. From where you end up, go north and you'll fight the Team Flare Grunt, who has a level 46 Swalot. You can't avoid this battle even if you use the tile south of the Grunt, because the arrows will push you in front of the Grunt in the end.
You can't get any farther here, so step on the round warp tile. You'll end up in an area with the Team Flare scientist Aliana. Talk to her to start the battle. She has a level 46 Mightyena and a level 48 Druddigon.
After the battle, she admits that she doesn't have the Elevator Key, but she'll step aside so you can use the warp panels. The one on the upper right (the yellow one) goes back to the entrance, while the one on the upper left (the green one) goes to the next area of the lab.
When you use the warp panel to the left of Aliana, go north and step on the arrow tile. You'll end up near a Team Flare Grunt that has a level 45 Swalot and a level 43 Liepard.
There's a door north of this Team Flare Grunt. Go into the door. You find the "mysterious" masked duo you encountered earlier. They're looking for a really tall guy that Team Flare is also looking for. You get some Revives from the masked duo. They admit that "a certain professor" sent them to stop Team Flare.
Now leave the room. There is only one way that you can actually go: step on the arrow tile to the right of the Team Flare Grunt, near the door that you just came out of. After that, the only way to go is to use the arrow tile south of you. You'll pass by a Team Flare Grunt as you are pushed south.
First, you should go into the door on the left. Talk to the first Team Flare Grunt to get TM12 Taunt.
Pick up the Revive that is sitting between the beds.
Check on a bed to heal up your pokémon. Then leave the room.
If you want to battle, talk to the Grunt to the east of the door where you took a nap. The Grunt has a level 44 Liepard and a level 44 Mightyena.
You can reach the exit if you go to the right of that Grunt and go south to use the arrow tile down there.
Otherwise, go back to the room with the beds if you want to heal after the battle, then go east from the Grunt.
The next Grunt in your way is to the east. This Grunt has a level 44 Houndoom and a level 44 Toxicroak.
Go to the right of the Grunt and step on the arrow tile that points to the right. You'll be pushed around to a bunch of different arrow tiles. When you finally stop, use the arrow tile to the right.
You'll end up close to a Team Flare Grunt who has a level 43 Manectric and a level 45 Scrafty.
Fight Celosia and Bryony
Go into the door north of that Grunt. Celosia and Bryony are here. As soon as you walk up to them, battle begins. You have to battle each one separately (not a double battle). You don't get a break to heal between.
First Celosia attacks you. Celosia is the purple-haired one (on the left). She has a level 46 Manectric and a level 48 Drapion. Both are weak to Ground.
Bryony is the green-haired one (on the right). She has a level 46 Liepard and a level 48 Bisharp. Both are weak to Fighting.
After the battle, Celosia and Bryony explain Team Flare's plans.
Now leave the room. Use the leftmost arrow tile that points downward. Carefully walk southwest without stepping on any arrow tiles. Eventually you find a warp tile to the southwest. Step on it.
From where you end up, go left and get the Black Glasses.
To the north, the Team Flare Grunt has a level 43 Mightyena and a level 44 Toxicroak.
Step on the warp tile to the left, then go north into the room. Go up to the top to find a Rare Candy. You can read the books in the shelves and the report on the table if you wish. You'll learn about the ancient king of Kalos, known as AZ. When you're done, go south and exit the room, then use the warp tile.
Now use the arrow tile to the left. When you stop spinning, go to the right and use the arrow tile to the right of the Grunt. When you stop spinning, use the warp tile nearby to get a Hyper Potion. Use the warp tile to go back to where you were.
Use the rightmost downward arrow tile south of the warp tile that you came from. (If you use the left one, you'll go back to where you began.) The Grunt to the right has a level 46 Golbat.
Use the round warp tile just north of that Grunt. You end up to the left of another Grunt. This Grunt has a level 44 Toxicroak and a level 44 Liepard.
After the battle, go east into the door. In this room, you find Mable. She has a level 46 Houndoom and a level 48 Weavile.
After the battle, she gives you the Elevator Key.
Use the Elevator
Leave the room where you found Mable, then go south and step on the arrow tile that is pointing to the left. After that, use the rightmost downward arrow tile. From there, go left until you are near the elevator. Step on the downward arrow to reach it. You can leave the lab and heal up at the Pokémon Center if you wish. Then use the elevator in Lysandre Labs.
Meet a Familiar Face
When the elevator drops you off, go west. You will discover that Lysandre has a familiar person behind bars. This is the same man you saw in Lumiose Badlands. He tells you a long story from the past. Afterward, the man warns that the ultimate weapon should not be used again, and he tells you to get the key back from Lysandre.
Lysandre tells you to follow him. Go east to the elevator and take it down to B3.
When you arrive in B3, go west and then north. You'll find Lysandre and Xerosic. They are about to activate the ultimate weapon. Lysandre says that what happens next depends on your potential. Xerosic challenges you to a battle.
Xerosic has a level 46 Crobat and a level 48 Malamar.
Press the Button
Xerosic tells you to press either the red button or the blue button. Which button should you press? The outcome is the same either way, but pressing the blue button is the "good" choice.
Go to Geosenge Town
As you saw, the Ultimate Weapon was activated in Geosenge Town. You need to go there now to try to stop the Ultimate Weapon from being fired.
In town, go to the northwest area to find a Team Flare Grunt. This Grunt has a level 45 Manectric (weak to Ground), a level 45 Scrafty (weak to Fighting, Flying, and Fairy), and a level 45 Golbat (weak to Rock, Electric, Psychic, and Ice).
The Grunt runs northwest after the defeat. Follow that Grunt. Your neighbor will run up and ask to accompany you. Go north and you'll arrive at the entrance to Team Flare HQ.