With c-lightning there are no restrictions to use as many as you want LN nodes with single bitcoind (i am hosting LN nodes as a service, and by default these use one single bitcoind, just with different RPC credentials).
I would like to point to these instructions: https://github.com/lightningnetwork/lnd/blob/master/docs/INSTALL.md#using-bitcoind-or-litecoind
Don't connect more than two or three instances of lnd to bitcoind. With the default bitcoind settings, having more than one instance of lnd, or lnd plus any application that consumes the RPC could cause lnd to miss crucial updates from the backend.
I think this is related to ZMQ. But i am not sure.
I am not aware how it is with Eclair.
P.S. I would like to to take this question as well as other one to shill my own service: i am offering full bitcoind nodes (TOR, txindex and other features), as well as ready-to-go c-lighting nodes - both just for 66 sats per hour (<4$/month) on https://bitclouds.sh . Check it out, it is way how you can cheaply use dedicated bitcoind (non-custodial, keys and configs under your control) for each your LN node. Also, good opportunity to try c-lightning (which i prefer more :P) without messing with configuration