As far as I understand, self-custody means personally holding the private key that gives you access to your onchain bitcoins.

A Lightning node also holds private keys, but in addition it maintains the channel state, including the current balance of the channel. If your channel peer agrees to close the channel, both parties’ respective balances are settled back to their on-chain addresses.

In my view, on-chain self-custody and Lightning self-custody are essentially identical when it comes to overall network health. In both cases you hold your own keys and contribute to decentralization.

The key difference is the security model: the private key of a Lightning node must remain on a server that is always online, which makes it significantly more exposed.

Ultimately, though, it’s up to each individual to decide what level of risk and convenience they are comfortable with.

Or is any part of my understanding incorrect?