You have to have an public IP and a computer that will work during hosting servers. If you have public IP and it won't work you have to open server ports on your router.
Have you opened the ports for LFS? Any firewalls restricting LFS' communication?
If you have Windows firewall activated or a firewall with the antivirus software, make sure LFS is in the exemption list. Look for the Program Permissions in the Firewall settings. Make sure LFS.exe is in that list.
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To do this, go to http://www.portforward.com/. Find your router make/model. On the next page, there is a link on the top right corner "Click here to skip this advertisemet advertisement...", click it. Find the Live For Speed Server on the next page. The resulting page got a guide on how to port-forward on your specific router.