If you look at the last line in the description of the Data Library of Alexandria, it says "which is added to the character's Lifestyle cost". This goes along with my understanding of it being part of your Lifestyle and thus attached to a fake SIN, which holds the account's credentials and login information. This means a TM can connect via their Living Persona just as easily as anyone else; it's just another part of the matrix to browse, once paid for.
