Her plan you thwarted was to be forever with the objects of her obsession.
Lusamine had an obsession with those Ultra Beasts since before her children were born. They were so far from her grasp that they seemed untouchable in their beauty. The grass is always greener on the other side. She had a child so she could dress them up in the Ultra Beast's image. First she had Gladion, but she wanted a girl to dress up instead, so she had Lillie.
Lillie was always dressed up like the Nihilego, and Lusamine herself wanted to be Pheromosa, because those were, in her mind, the most beautiful creations to have existed.
Gladion was never babied, which is why he had no problem jumping straight into battle as a trainer after learning what was going on with Type: Null. Note that she never thought Gladion was beautiful. She liked Hau because he had big shoes to fill -- just like Lillie did.
"Nihil" means "no." "Nihilego" means "no ego," or "no identity." The Nihilego are the enemy.
Over the course of the journey, Lillie had been seen near clothing stores, practically yearning for an identity of her own. And only when she stepped out of the image she was painted into did her mother realize how much more beautiful she was than what she'd previously been obsessed with.
It's a story about individuality and different ways people deal with it. Hau is coping with being in a shadow constructively. Guzma is coping with the shadow destructively. Gladion copes by going at it alone. Lillie needs help from the protagonist getting there.
The moral is to be yourself. It doesn't matter what someone told you you can and can't do. You're most beautiful as your own person, not as something someone else wanted you to be.
