The way I get lucky eggs takes a short while to start up, but the results are worth it.
1. Go to the Pastoria Marsh and start a Pokemon Catching game. Catch a Yanma with the ability Compoundeyes, as this increases the chances of encountering a Pokemon with an item. Alternatively, you could catch one of the other Pokemon that have this ability. (Butterfree, Venonat, Dustox, Nincada)
2. Go to the Old Chateau in Eterna Forest and catch Rotom. Go to the Move Teacher/Rememberer in Pastoria with a Heart Scale (found in the Underground) and replace one of his moves with Trick. This will allow you to switch held items with other Pokemon in battle. You could also catch another Pokemon that can learn trick, (Kadabra, Alakazam, Mr. Mime, Mime Jr., Shuppet, or Banette) however, these Pokemon learn it at high levels.
3. Go to the route above Solaceon Town with Yanma (or your Compoundeyes Pokemon) leading. When you finally encounter a Chansey, switch to your Trick Pokemon and use it. You will most likely get an Oval Stone, (Used for evolving Happiny) but stick at it.
I have gotten over a dozen Oval Stones and five or so Lucky Eggs using this method.
Note: Some people suggest going to Mr. Backlot and softresetting until he says he had seen a Chansey. I have not yet tried this.
Chat with our AI personalities
When you catch a Chansey, there's a chance it's holding a lucky egg. I have gotten several.
The lucky egg is an item that doubles the amount of exp that a Pokemon gives. You can get it from a Chansey if you are lucky (found near Solaceon town).
Transfer in a pokémon that is holding a Lucky Egg.
Nothin' hatches from a Lucky Egg......I WISH SOMETHIN' DID!
you get it from an egg in Pokemon platinum