The concept of a 'single point of truth' comes into play here.
For some given piece of data, there needs to be just one place in your architecture that holds the definitive state of that piece of data.
Some examples of how this can be achieved:
* A database that is shared across the application servers.
* Sessions that are serializable and can be moved to whichever application server processes the request. Some kind of fast distributed store may be used for this purpose.
* Sticky sessions. The same sessions always comes back to the same server, making it simpler to guarantee a single point of truth.