You’re on the right track! It's free to run a node on both the Bitcoin network and Lightning Network. However, running a Bitcoin node can require more resources (like storage for the entire blockchain).

Now, onto your question about how it works on the Lightning Network!

Running a Lightning node involves keeping track of off-chain transactions in payment channels. You'll need some bitcoin to open these channels. When someone wants to make a transaction that passes through your channel, they pay you a small fee.

So while it's "free" in that there's no cost to simply run the software, you do need some BTC if you want to participate fully and earn fees.

Hope this helps clarify things!