Okay. So as you probably know, a Lucky Egg is a rare item that Chansey holds that boosts the exp of the holder by 50%. However most Chansey hold Oval Stones. I will show you in this guide the easy way of how to get one!
First, you must have:
1. defeated the Pokemon League
2. Received the National Pokedex
So first, you have to go to the Trophy garden and "make" Mr. Backlot find Chansey in his garden! To do this you save in front of him, and just keep on soft resetting (pressing L, R, Select & start at the same time) until he sees a Chansey!
You will need a Banette (or Stantler) with the Frisk trait and a Nincada or Butterfree, for the Compound Eyes trait at level 18! Why 18? Because that's the same level that Chansey's at. You must have this pokemon in the first slot of your party. If you do, then a chances of the wild pokemon that you encounter has a massive 50% chance of holding an item! Having a Smoke Ball on that pokemon may help as well, to escape battles more easily. Use Repels to stop any other pokemon from coming up.
So, once you find the Chansey, then you have three choices:
1. Catch it
2. use Covet or Thief to steal the Egg
3. Use Trick or Switcheroo to swap your item with the Lucky Egg!
If you are planning to catch the Chansey, then it will be useful to have a pokemon with Flase Swipe or Super Fang to get her HP down. Any status moves (besides burn and poison) could be helpful too, but Sleep is the number one choice because of Chansey's refresh. A pokemon that has Heal Block might help so Chansey won't be able to heal herslef with Softboiled!
If you are going to steal the Egg, make sure you don't have an item already attached to your pokemon, then after you find the Chansey switch out to that pokemon, then just use Covet or Thief. If you're aiming for more than one Egg then make sure you take the egg that you stole off of your pokemon or else it will not be able to steal the egg!
That's about it... I just wrote this guide because I was bored. :P
I hope this helps, and Happy Hunting!