If your LMCE core is exposed directly on the internet (ie it isn't behind a broadband router) then you can ping it, but you won't receive replies because of the LMCE firewall. I don't believe you can turn on ICMP Echo (pings) in the Web Admin but almost certainly you can using the command line interface.
If your core is behind a broadband router then your core is probably on a "private" IP subnet like 192.168.x.y in which case you are attempting to ping the router (which owns the public IP address) not the Core, and these are almost always set to drop ICMP packets.
Need to know whether the Core is actually on the Internet directly first, or behind a router, before I can help with your VoIP.