Lilly taught all his Pokegirls Occlumency to learn faster, think clearer, and protect their minds. She also taught her Harry beyond the mind melding they both did. This allowed him to find and basically eat all the information that Tom had at that point. When Harry downloaded the info from Tom, they made plans for when the school contacted him. They were still thinking about weather to force them to accept her in his year, or to use her as a free agent. This would allow others to watch him, while Lily took care of the Locket and Ring, while he did the Tiara. She could then use it.
They decided to wait for her. The reason is the girls would be a year younger and Lilly wanted to get them into the family, coven, or harem of her Harry! She put the machine together and found out that it could produce different balls than just the normal ones. But to do so, they had to make ten normal level ones. That allowed them to make a specialized level three., Futas They had to make five level threes to make the super specialized level fives, girls that look human, high sex libidos and elemental powers times three. After getting info on that she found that it takes making ten sex balls to be able to make a legendary ball.
This means a Queenball, a Mew ball, or other Legendary Pokemon. The thing is, they are always female Pokegirls. Lilly plans on Alice's and Molly's daughters being Legendary, maybe Queens also to her Harry! As she does not think of them as her daughters, but Harry's girls. Because of the info from Diagon Alley, she thinks that Harry should take the Malfoys (Futa Ball the males) and bring in the Bones.