[S/M] can you pickup lucky eggs?

[laelaps90]

I've lost mine on GTS and heard you can use your Pokemon's pickup ability to get another one. So far I've heard just as many people say it's true as false do any of you know?

[Najar23]

I dont think it's true, i also lost mine on GTS, i was trying to snipe a shiny pokemon and through my quickness i forgot to remove the lucky egg from the pokemon