Is there any way to prevent (low-level) Pokemon in the daycare from learning new moves? This is for egg move breeding purposes.
There's no way to "lock" the moves the Pokemon goes in with and prevent it from learning level-up moves in the daycare, but luckily for X and Y, the moves a Pokemon passes down to eggs are set the moment it's put into the daycare. So if your mon goes into the daycare knowing everything it needs to pass down, it doesn't matter how many levels it gains. how many new moves it learns or how often it overwrites the moves it had before, every egg that it produces will hatch with the same egg moves the parent went into the daycare knowing as long as you don't remove said parent.
The moves Pokémon learn while in Day Care are also based solely on level-up: if a Pokémon is raised to a level at which a new move would be learned, the topmost move in its current moveset will be deleted, and the new move will be placed at the bottom of the moveset.
Source.
1* track their daycare growth and take them out every so often to rearrange their movelist so the egg moves remain on the bottom
Unfortunately, there is no way. However, the great thing about the Move Relearner is that if the Pokemon had known the move legally at one point of their lives, the Move Relearner can bring the moves back, so its all good. This applies to event moves as well.
So really, there's nothing to worry about.
Hope I helped. :) Source: http://www.gamefaqs.com/boards/696959-pokemon-x/67627455
