do you know the difference between bank balance euros and settled withdrawal of physically exchanged dollars
the LN payments are millisats(bitcoin network does not understand). and is LATER hours/days/months settled by negotiating contract terms of fee's and rounding up/down of millisats into a bitcoin value.

you may not notice it at GUI level. but at code/raw data level you will see the negotiation of exchange of units of measure.

whats next.. if a exchange/western union took in FIAT, but behind the scenes used crypto to do the reserves transfer between different WU 'shops' you will claim that crypto is fiat, under the naive beleif that all the customer can see is the fiat being settled.

no, when you understand the inter-change happening in between you then realise the separate mediums of exchange happening and the contract and reserve values change and the negotiation of conversion from one unit of measure to another happen. then you start to see that the customer facing view looks like its a fiat transfer system, but then realise that its a fiat-crypto-fiat system and they are separate systems, not to be confused with each other and definitely not to be used to pretend that crypto is fiat

if LN was bitcoin. then LN can only be bitcoin. it could not be anything else. ..
but LN is its own separate thing, which is why it allows different cryptos to peg to it.

but the first step to understanding it is to realise that bitcoin does not leave the blockchain. the value is locked to the blockchain. all the negotiated off-chain stuff  measured in units not understood by bitcoin are not bitcoin things.