Yes, it is on a Pokemon. A Chansey, to exact.
However, there is a catch. For every Chansey you encounter, there only a 5% chansey (not sorry for this, lol) that the Chansey will be holding a Lucky Egg.
That's the hard bit:
Now, I'd recommend you to actually migrate one from a previous generation (from R/S/E or FR/LG, i.e., Generation III specifically). Unfortunately, if you can't, you're in for a bit of struggle from here on, because the most legitimate and guaranteed method is very, very redundant and taxing. Proceed further only if you're willing to spend a good bit of your time onto this.
Steps to get a Lucky Egg (to quote a perfectly written [WikiHow]):
- Acquire a Pokemon with the "Compound Eyes" ability (recommended)
- Acquire a Pokemon with Frisk (optional),
- Acquire a Pokemon with either False Swipe (to make catching it easier) or Thief (so you can just steal it afterward)
- Go to Route 209.
- Encounter a Chansey using Pokeradar *
- Fight (or capture) each Chansey you get, and it might be holding a Lucky Egg. You can check its held item with the ability "Frisk" or, you could use the move Thief to acquire it without having to catch it.
- $$$$ Profit $$$$
>*Use the Poke Radar until you find a Chansey. Afterwards, bring out the Pokemon with Frisk, and if it has Lucky Egg, either catch it or use Thief. If it doesn't, knock it out and repeat. Remember to take the Lucky Egg off after using Thief.
Beware other wild Pokemon other than Chansey that could break your streak, though.
Okay, sorry that last bit was a joke. Either you catch the Chansey and get the Lucky Egg or use Thief. Remember though, that this is very tiresome and repetitive work.
>Make sure your first Pokemon (the one with Compound Eyes) are both at least Level 21, because you will need it to make sure the Repels will prevent your Poke Radar from breaking streak.
Pokemon that know Frisk are : Bannette, Stantler