How could we improve privacy on Lightning? How important is this in your opinion?
It is important.
Sender privacy is already pretty good.
Receiver privacy is not that good (since the has to know the receiver's node) but IMO not that important for businesses. For personal use there are wallets that have implemented "fake" (i.e. rotating) pubkeys per payment, or you just use one wallet for receiving funds and then move the funds away to your "real" wallet.
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