Users are not able to edit the web page on web server while traffic passes through the Load Balancer

It's difficult to say without knowing more about the application. It's also certainly possible that some kinds of access are blocked through the load balancer because of authentication requirements or other proxy-related issues. I think the next step in troubleshooting this needs to be a comparison of the communicated protocol data across the two paths. The easiest approach would probably be a client side capture process like Fiddler or HTTPWatch. What you're looking for, essentially, is a marked differences between the two paths. You might see an authorization header in the direct path that you don't see in the other. You might see the app sending absolute references to itself (and local objects) using its internal name. Specifically look at what happens when you engage the edit function(s).

Please report back what you find.