Does Taproot pave the way for lightning network?
Lightning Network only makes sense if everybody accepts it as payment from your local coffee shop to Amazon right?
taproot can make LN settlement commitments cheaper.. IF the channel partners use the same subset of keys
from the same keyseed.
it works by using a RANGE instead of a point. meaning multiple keys or a mathematic average of those keys are within the range of the needed proof range
its useful if one user wants to generate a thousand public addresses from a seed knowing that it only needs 1 signature to prove them all when spending all the funds received on those addresses
it doesnt work if people are generating keys from completely different random points unassociated with each other in any way. EG different seeds from different wallets
there might be 'some' LN utility for what is known as 'LN watchtowers/factory' services which is where there is a manager(third party) that sets up the channels on behalf of 2 users. whereby its always the watchtower/factory that is broadcasting the commitment.(lite wallet app ->manager server)
but in those cases. most of the time the factory is just aggregating balances offchain and resetting up new channels without needing to broadcast.
but in short.
it wont make LN any better. but does allow more oppertunity for managed channels(with pros and cons of that)
but mainly individuals can seed thousands of addresses and need only one signature
say for instance. exchanges/pools making batch payments