I meant, isn't it possible to develop privacy features to hide sender, receiver, and amount, off-chain in the Lightning Network?
Nodes participating in the routing process don't know who initiated the transaction and what the final destination is thanks to
onion routing. Transactions are not listed anywhere so they can't be tracked by outsiders. As for hiding the amount, multi-part payments
have just become a real thing.
For hiding amounts and CLTV deltas, C-lightning also uses shadow routing.
OK, with all that, can Lightning then be developed into a viable, trust-minimized alternative for centralized mixing/tumbling?
As I said above not really if you want to get back on chain afterwards. But just use joinmarket if you want trustless mixing...
Even at low LN-fees, I assume nodes will charge a percentage because that's how they earn (and they need to balance their channels again), so for high amounts, on-chain fees will be much lower.
It depends, I expect most of routing nodes to remove (most of?) their base fee in the future, and thus thanks to multi part payments you could make big payments as well.
As the network grows there will be more and more alternative paths from you to your destination (and even more with smaller payments if you use MPP!), and if some node owners rise their fees too much they wont be chosen into routes anymore. So I don't expect fees to rise that much.
Nonetheless I hope the base layer will still be used because...