LN is not consensus locked to bitcoin.
LN dies not even have a consensus
this is what some call a feature but is also a flaw of LN, because LN can be broke very easily and also changed very easily to fit any network
LN devs can(well their dev politics agenda is a different story) . anyway the LN devs can have a set up of channels where instead of having pegged sats to msat. they can have pegged stable coin to pegged mcents
the same way bitocin, litecoin, vertcoin(and others) lock value to an utxo. and hen use that as a reference point on LN to then make 'commitments' and then 'payments' in msat balance
there are stable coins that could do the same. have a lock where their utxo dont move unless terms a re met. and hen use that as a reference to create the mcent channels