I had never noticed before that I can't seem to get them in the Pokémon center in Lumiose before, either. But I don't buy Heart Scales, and I only spend Pokémiles on the Global Link website. I'm going to back up, and explain this entire thing from the top. I will explain Luvdisc Farming first, but then the Global Link system - skip down past the Farming section if you just want to read about the Global Link.
Heart Scales - what they are and how to get them in Pokémon X and Y
Heart Scales are an item with no real effect, introduced in third-generation games, with no in-game effect. But, if you give one to the Move Reminder in Dendemille Town, she will re-teach your Pokémon a forgotten move - including certain moves that can only be learned this way (a notable example in this generation being Aegislash's King's Shield).
As I've mentioned before, Luvdisc often hold Heart Scales. Some people will catch large amounts of Luvdisc, harvesting the items from the PC - but my preferred method is to use the move Thief to steal them. Thief is available as TM46, given to you by a woman in Cassius' House in Camphrier Town.
The best users of the move Thief are Pokémon with the ability Frisk - which alerts you at the beginning of the battle as to whether the enemy is holding an item, and what it is. Frisk can easily be found on a Pumpkaboo, Phantump, or Noibat. All three of these Pokémon can learn Thief via TM46.
Efficiently Farming Luvdisc
Cyllage City is probably the best place in the game to fish for Luvdisc. Luvdisc is the only Pokémon that will bite if you use an Old Rod. Simply fish, leading with your Thief. If the Luvdisc has a Heart Scale, steal it. If not, run.
An extra trick - Compound Eyes
If a Pokémon with Compound Eyes is leading your party, wild Pokémon will be more likely to be holding an item. This works even if the Pokémon with Compound Eyes is Fainted - so, having a Fainted Compound Eyes Pokémon in the lead of your party and a Thief in the second position can make farming even easier, with the cost of having to intentionally knock out one of your Pokémon to do it. Easy to obtain Compound Eyes Pokémon include Butterfree, Yanma, Nincada, Scatterbug, and Vivillon.
Global Link - Online Shopping with Pokémiles
As briefly discussed in the lead of the post, there is a man in the Pokémon Center on South Boulevard, Lumiose City who will sell you certain items (that link goes to Serebii) for Pokémiles - which are obtained in a small quantity by walking around Kalos, but much more quickly by trading with people around the world - whether on the GTS or on Wonder Trade!
Now, I don't shop in Lumiose, because everything you can buy there, you can buy cheaper in the real-world Internet, by using Game Sync. This all works by playing Online, using a Wi-Fi connection - same as Friend Safari.
To use Game Sync - you'll first need to create a Pokémon Trainer Club account at pokemon-gl.com. If you already have one from 5th Gen (where this was necessary to access the Dream World), you simply have to register your new cartridge.
Your Game Sync ID, which will be needed to register your cartridge, can be found through the second page of your start menu, by the GTS and Wonder Trade options. Once you configure your Game Sync, you'll be able to send all your Pokémiles to the Pokémon Global Link - where you can buy any item they sell there for significantly cheaper than the Lumiose Price. This includes Heart Scales, for 100 miles each. Just go to the Pokémilage Club and spend your Pokémiles! When you're done there, Game Sync again, and a courier will be waiting for you in any Pokémon Center in the game with your merchandise.
I hope this helps some of you on your quest for Heart Scales, or other rare in-game items - such as Rare Candies (250 Pokémiles on Game Link) or PP Ups (500 Pokémiles)!