What are requirements for a web application to work in a cluster environment

I need to check if existing web application is ready the be deployed in a clustered environment.
Cluster:
Several Linux boxes. The flow is controlled by a load balancer that is using simple round robin algorithm with sticky session.
Application Stateless (hopefully) java web application that retrieves content from back office and format it appropriately.

I have access to the source code. What should I check in the code to be sure that it will run in the cluster?

• Check that something is not cached in a memory or file system that stores state of the application.
• ...Something else?