It might be a difference on which type of computer you're on, some have different private networks. Perhaps it's NAT adresses? or router IP adresses, that's what I see used in CS2D.
to answer the question in the title: of course it is NOT possible to get the internet IP just be knowing the LAN ip because LAN ips are NOT unique. there can be (and there are) 1 mio pcs with the same LAN ip.
and I also can't find this server in the serverlist so you didn't setup router/firewall stuff correctly.
when you see it on YOUR computer in lan then you can open this website from YOUR pc http://www.cs2d.com/faq.php?show=net_ip#net_ip
and this IP will also be the IP of the server. otherwise you wouldn't see it in your LAN tab.
still possible that no one else can join because of wrong router/firewall settings
(yes, connecting over the LAN has other "requirements" than connecting over the internet)