Is it possible to run two Lightning Network nodes on top of single Bitcoin Core node?
Technically it should be possible. You can find a pretty straight forward description in the lnd docs at: https://dev.lightning.community/tutorial/01-lncli/index.html

I am running several c-lightning nodes on top of the one Bitcoin node that I'm running. In clightning you just have to specify a different data directory and port for each node. Also on this machine I have an lnd node running. 

I could give you examples how to do this with c Lightning but you asked for lnd / eclair. As said I don't see any reason why it would not work with the other implementations but I have not checked it yet. This referring you to their documentation.