SPOILER WARNING
In order to get Lien's route, you need to complete all the others, which means completing Xanthe's route first. You'll get a little vampire teddy bear when you finish Xanthe's route and thats when you can complete Lien's! (And as for the main menu items, the cat is for Lyell, the cassette is for Bae, and the bracelet is for Victoria!)
Hope this helps, but lmk if you have more questions :D