I am considering using Unity to manage the lifetime of a custom user class instance. I am planning on extending the LifetimeManager with a custom ASP.NET session manager.
My apologies if this isn't quite right but ...
Unity is a game dev platform, therefore I assume that you are building a 3d app or game that you intend to do something cool with (e.g. make it multiplayer / track users progress using the server).
Why not have each user login, then you can use the MembershipProvider and Formsauthentication classes to gain acces to the users id / name.
On your server you simply link all information to that for the user allowing you easily pull back (simple ajax / normal http request) data relevant to the situation / users request.
I don't know this for sure but i believe that unity is something that deploys client side therefore no integration with it needs to be done on the server.
Simply request what you need and process it on the client side.
That way you stick to the classic n-tier design pattern that allows you separate your logic from your data storage and ui.
Hope this helps ...