If you are using dummy IPs and/or VLANs then yes, LMHOSTS is a viable solution (make sure you include your #PRE and DOM as well). Note also that Tracy is correct in mentioning the security problem. If you have it avilable, WINS is the better solution.

The reason you are abale to use the IP to map the share is because the network equipment understands the routes to get your packets where they need to go. Because you are using dummy IPs though, NetBIOS is not available; hence why you can't use the computer host name. By utilzing LMHOSTS (or WINS, firewall, etc.), you are associating the IP with a text name.