I had a similar situation in my current project, the way I did it was to pass the UserID as a parameter from the MVC project into any method I used in the class library.
EDIT
public int ClassLibraryMethod(your parameters, **string userId**){}
Now from whatever class you are working from in your MVC project, you can call User.Identity.Name, assign it to a variable, and pass it along through your class library methods for use.
string userId = User.Identity.Name;
var lib = new ClassLibrary();
lib.ClassLibraryMethod(your data here, userId){}
This will allow you to get the userId from the MVC project through your methods.