Lillie does it unconsciously now. After training sessions, she'll kneel with outstretched arms, and Snowy will leap into them without hesitation, making her giggle. Often Lillie even wants to hold Snowy for longer, when she's struck by how small Snowy is compared to pokemon like Turtonator. And Lillie will worry, just as she worried over that breakable egg, kept it on soft pillows and fretted about cracks.
But then she'll see Snowy loose a Powder Snow that could stop Turtonator in its tracks, or perform a Tackle that could surprise even Pikachu, and remember that Snowy's not an egg anymore.