After going east through Brun Way, you can go down the stairs of the eastern ruins to reach the Lost Hotel.
Before you visit the Route 15 side of Lost Hotel, you might want to go back to Lumiose City and talk to the roller skaters in North Boulevard, and in Café Rouleau (on Estival Avenue). You'll learn some tricks from them, which unlocks a new trick that you can learn in the Lost Hotel.
As you walk around the Lost Hotel, you might encounter wild pokémon, including Magneton, Electrode, Litwick, Pawniard, and Kefki. Also, only at night, the green trash cans might shake. If the trash cans aren't shaking, come back when it's night time. Check on the shaking trash can to find an item or make a wild pokémon come out. Normally, a Trubbish or a Garbodor pops out, but on Tuesdays, you might encounter Rotom. If you catch Rotom, you can change its form by going to Professor Sycamore's Lab in Lumiose City and checking on the boxes in the corner.
In the Route 15 entrance of the Lost Hotel, Punk Guy Sid is near the entrance. He will battle you. He has a level 39 Scrafty, a level 39 Sharpedo, and a level 39 Pawniard.
If you keep going south, you'll encounter Punk Girl Jeanne, who has a level 40 Seviper and a level 40 Arbok.
South of the Punk Girl, you find a Smoke Ball.
Go north from the Punk Girl, then west. To the west, Punk Couple Zoya & Asa challenge you to a double battle. They have a level 42 Pangoro and level 42 Garbodor.
Keep going west until you reach a Punk Girl and a trash can. Go north. If you have learned the skating tricks from the skaters in Lumiose City (see the "Skate Tricks" section at the top of the page) The Punk Guy will send you to talk to Boss. He'll teach you the cosmic flip. To perform it, you have to jump from a ledge while doing a drift and dash. The drift and dash is performed by quickly skating in the opposite direction. So you have to skate away from the ledge, then quickly change direction toward the ledge to hop off and do a cosmic flip.
Go east and use Rock Smash on the cracked wall to get TM95 Snarl.
Leave the room where you got Snarl and go east to get a Twisted Spoon. If a pokémon holds a Twisted Spoon, that pokémon's Psychic attacks will be 20% stronger.
To explore the rest of the hotel, go south from the Route 15 entrance to the Lost Hotel until you reach Route 16. Use Strength to push the boulder out of the way. The Lost Hotel entrance is in the ruins near where you enter Route 16 from the north.
When you enter the Lost Hotel from the Route 16 entrance. You find Punk Guy Slater running around. He has a level 42 Dunsparce.
The first cracked wall in this hallway doesn't lead to anything, but break the second one with Rock Smash to get a Dread Plate.
Keep going west. There is another cracked wall that can be knocked down with Rock Smash, but there is also nothing behind it. Go west past it to find a roller skater who will give you TM56 Fling.
Go east from the roller skater, then go north. You find Punk Guy Jacques running around. He has a level 40 Skuntank and a level 40 Crawdaunt.
East of Jacques, there is a trash can. You can check on it in case a pokémon is hiding in it.
Go north, then west. You find Punk Girl Cecile. She has a level 40 Liepard, and another level 40 Liepard.
Go south from the Punk Girl and crack the wall on the right with Rock Smash to get a Protector. If you trade a Rhydon that is holding a Protector, it evolves into Rhyperior.
Now you have found everything in the southern half of the Lost Hotel, so you can use an Escape Rope or go back to the entrance.