In a Lightning channel, your funds are split between you and the counterparty. For a 10M sat channel where you hold 5M sats, your 5M is locked to you and cannot move to the other side unless you sign a transaction to update the channel state.
Your private key doesn’t directly “hold” the funds but is essential for signing updates to the channel state. The channel funds are locked in a multi-signature address on the Bitcoin blockchain, and both parties must sign to update or close the channel.
Self-custody here means you control your private keys, so you have full authority over your funds and can close the channel at any time to claim your portion on-chain. Tools like OneKey make managing this easier by securely storing your keys.