I have the feeling that load balancers will have a hard time detecting a UniGUI browser session
and dispatching calls from the same browser session to the same back-end server.
The reason is that UniGUI does not use cookies - instead it puts the session id in each request.
Two workarounds come to my mind:
1) configure the load balancer to dispatch among the available back-end servers based on the browser IP address
2) modify UniGUI to set a cookie named JSESSIONID in the browser, without actually using it.
This is what Tomcat does, and it should trigger Java-compatible load balancers into using "cookie based stickyness"
i.e. always dispatch to the same server all requests containing a JSESSIONID cookie with the same contents.
Of course any decent load balancer will have the option to configure the name of the cookie used for stickyness.
See for example
https://httpd.apache.org/docs/2.4/mod/mod_proxy_balancer.html#stickyness
https://httpd.apache.org/docs/2.4/mod/mod_proxy_balancer.html#stickyness_implementation