She had read about it in a book in her dimensional space; it's said, that the Nine Tailed Silver Fox is protective by nature. They have a bond in their souls, meaning that they can find each other while following their soul's tracing. If the cub is in danger, the parents will rush towards their child. And if they found out that Lu Yang had been training their cub to become powerful, they will feel grateful towards him, and they will compensate for his efforts.
Xiao Ling had come with this plan when she saw it was a Nine Tailed Silver Fox's cub. She can have the cub, and her first senior brother can have his own legendary beast.
Lu Yang did not know what his precious Junior sister was thinking, he only knew that she entrusted him with her new pet, to train it to become powerful enough to protect her. With that in mind, he could take the responsibility to train harder the cub.