it's possible and I'm sure there are wallets that do it all bundled into one. But if you are talking about holding more money in Bitcoin than you can afford to lose, you need to have a full self-custody solution in place. One aspect of that, I would argue, would be to fully separate your LN from L1 system.

Your UXTOs on chain are where all of the value is. This is bitcoin, protect this at all costs.

LN is a payment convenience so you can pay P2P quickly and without messing with your UTXO set.