I recommend capturing it. TM32 Double Team.
Pick up the Black Glasses. Smash the rock and go inside the narrow passage to pick up a hidden Moon Stone. In this battle, Lysandre will Mega Evolve his Lv.
Not particularly useful, but it's there. The tall man tells his touching story in a cut scene. Go across the bridge and head southwest.
After the battle, head south to the previous warp panel, then head west until your each another Pokemon Trainer. Smash the rocks, battle the trainer, slide down the ramp on the east side, and pick up the Elixir. It takes some patience to catch legendary Pokemon, who are quite a bit harder to catch than your average Pokemon.
Head northwest to pick up an X Attack. Smash the rock and head all the way west for a Dusk Stone.
Once you go inside, step into the middle and the gym transforms into crazy rings of paths and teleportation tiles. You'll be spun around for quite a while. However, this item doesn't do anything.
A woman inside this Pokemon Center will give you one of four Technical Machines depending on the time of day you speak with her. Go into the room and you'll fight two more Team Flare members. Head east for a Reaper Cloth. Lava Plume Bite Quick Attack. The Grunt inside will give you TM12 Taunt. Right before the bridge, smash the rock to pick up a Star Piece. The girl standing by the book shelf outside the Poke Mart will give you a different TM each day depending on the time of day.
Right outside is a Max Ether. Go north, fight the Grunt, and go into the room to get Revives from the vigilantes you met earlier. Bonding will give you an O-Power.