Suppose I have two Tomcat instances load balanced using BIGIP or other similar solution. If once Tomcat instance goes down while it was serving few request, what happens to those requests? User gets an error in browser?
It depends on what layer you're doing the load balancing. If it's at the IP layer, they'll probably get "Connection Reset By Peer" error, although the browser may display that in a "user-friendly" manner. Alternatively they may just get a timeout after a while. If you're doing HTTP proxying, you'll probably get a Bad Gateway response from the proxy. Either way, yes, you'll get an error in the browser, but presumably, assuming your load balancer has noticed the failure, any refresh will display the correct page. I'm not sure that there's a lot you can do about it. I think web users are conditioned to expect some failures from time to time.