The Lost Hotel is on Route 15 (also known as Brun way) in the Kalos region, next to the entrance to Dendemille town. One area of the Lost Hotel is blocked by a man who claims you have no style. To get the style you need to pass him, you must first learn the roller skate tricks in Lumoise City. Skaters throughout Lumoise City will teach you the tricks, though the two you must be taught are the backflip (talk to the skater next to a tree in the North Boulevard) and the 360 (talk to the skater inside the Cafe Rouleu off of Estival Avenue) A skater inside an office building on the western end of South Boulevard will tell you about the Parallel Swivel, and one next to the monument in Vert plaza will tell you of the Running Start (Drag n' Dash), but you can do both of these without talking to them.
The "Boss" of the Lost Hotel will teach another trick: the cosmic flip. Also, the Twisted Spoon and TM95 Snarl are in this area.