How can one form a friendship with someone in one's own mind? It's simply not possible. Sure, you can create any (false) personality for her that you wish, but...
You want a two-way relationship out of something that is and will always be entirely one-sided. It will only hurt.
Do not allow yourself to delve too deeply into your own fantisized image of Lia. Do not fall victim to infatuation. Many others here have.