If set latency from "Connection Emulator" and refresh page for Local Area Network, I was expecting that page response should be delayed by that much time. But its not giving any time difference in page load (checked this in firebug "NET" tab).
How to apply latency for any site running on my localhost?
There is no way to simulate latency or packet loss on a local host, because in a local host connection the kernel doesn't split it into individual packets and it never reaches the NDIS level.
If you want to simulate these on a local host, you can use a Virtual Machine to run either the server or the browser. In this case the VM would communicate with the host OS using its TCP/IP stack in full.