"How does running your own lightning node enable you to self custody lightning?"
because it gives you control of the funds without third-party services. you can open, close, and manage channels. final settlement occurs onchain so you keep your funds through the process.
"Do you also say running your own Bitcoin node enables you to self transact UTXOs as if the Bitcoin network isn't still required for valid transactions?"
requirement of an underlying network has no bearing on self-custody
^.^