Do you get errors or anything?
I use wamp (Windows here) and when it's running any device (tablets,phone,laptops,TV etc.) on the LAN can view sites hosted on my PC by browsing my LAN IP address. You can setup a name to acces the site, for example on my lan "http://localserver/" but lets start off slow.
Without know more about your setup that's all I can say right now.
At the moment (best explanation I can come up with)
I have a virtual host setup as "XXXXXXX:8889/" Which points to the folder where my index.html file is.
When I acess it from my computer which is running MAMP all is fine. When I try from the iPad I get a permissions error and the address displays as "http://www.XXXXXXXXX.com.
So I guess I am wondering how you set up your WAMP to do this and type in your virtual host and be taken to the live web site on your local network.
I al really bad at describing my problem so please be patient.