On DHCP server I changed DNS server for internal DNS resolving, this was acknowledged by all DHCP clients in network with exception of LibreElec client. At least after reboot even Windows got new DNS server.
Before this change DNS server were 8.8.8.8 and 8.8.4.4 - after change it was 192.168.3.15. Until that migration I abused my Internet DNS server for also resolving internal names, which is a bad idea from standpoint of security. After changing this, LibreElec was no longer able to to resolve internal servers. Tracking down the root cause brought me following file:
/storage/.cache/connman/ethernet_<mac address>_cable/settings:Nameservers=8.8.8.8;8.8.4.4;
which still held - bingo! - old DNS config. After changing this file with new DNS config by vi and reboot LibreElec resolved all internal servers.