Many thanks for you hint.

Adding the ip addresses to the host file doesn't solved the problem, but gives me the crucial hint to find the real problem.

Root cause was my BitDefender firewall. Allthough I use the same version on both of my systems, they behaved differently. After enabling ICMP requests (disable stealth mode in the BitDefender firewall) connections in both directions works.

Now I'm happily dual-boxing LOTRO on Maiar.