I always used this display in my wallets.
Is the most logic one.
Onchain you are doing transactions, that means bitcoin (with display 8 decimals). You are holding, not making payments.
On LN you are doing payments, that means you are dealing with sats. The whole LN system is using sats (not bitcoin) and even msats (mostly for fees).

It's the most logical way to deal with denominations. Not a single person uses BTC for LN, it's always sats.