User blog comment:Ncduru/Who is Anna?/@comment-4999650-20151211175244/@comment-9595671-20151212061727

I don't think she had all 12, she had 3 of the keys and gave them to people who'd give them to Lucy if she wanted to be a CS herself. If she had all 12 then Lucy would have started with more.

Karin herself shows that Layla likely didn't have all 12. She saw them as tools and didn't want to give up her two Gold Keys. I doubt Layla would give them to her due to how Karin saw CS's at the time.