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The problem initially is that the Lucky Egg is only a 5% find on a Chansey... and since Chansey is like 1% rarity in this game that leaves you with about 1:2000 chance to find a chansey with lucky egg if you're looking on the proper route. But you can catch a break:
With Chansey Swarms (today was my third...) Lucky Eggs are easy to get.
Here's what you need: Get a Pokemon with the "Compoundeyes" ability. I know Yanma and Butterfree have them, but there are others as well. Next, get a Pokemon with the "Frisk" ability. I know Shuppet and Stantler have them. And thirdly, get a Pokemon with the move Thief (Covet also works).
Compoundeyes increases the rate in which wild pokemon have held items. I don't know the % increase exactly, but it's very significant. Put the Compoundeyes pokemon leading your party. Head to Route 13 (this is the one, right?) during the Swarm. I wouldn't even bother trying unless it was Swarming, btw.
Next, when you do encounter the wild Chansey, switch your Compoundeyes pokemon with the one that has the Frisk ability. IF the wild chansey has an item, you will a message that reads: "<Pokemon> frisked Chansey and found one <item>." It will say either Lucky Egg, Oval Stone(this one is quite common), or it will say nothing at all. If it does not say any message at all, then the Chansey does not have a hold item.
If the Chansey does have the Lucky Egg, simply switch to the Pokemon with Thief/Covet (make sure it isnt already holding an item) and use the move. Done!
If it is swarming, that's really a free ticket to a Lucky Egg. I got like 6 in under an hour.
I had to catch 35 Chanseys until I got a Lucky Egg...>_< If you have the first set of objects in the Safari Zone, set up 12 Shrubberies in the Meadow and then have a Pokemon level 41-42 following you and use repels, so all you'll run into are Chansey. It not worth throwing bait or mud, just toss away with the Safari Balls. It's very time consuming so you have to be patient but it's the easiest way to find/catch a lot of Chansey.