Privacy on BTC lightning is basically:
- So-called good sender privacy (because in-between hop node does not expose from-node to the to-node). So AFAIK the sender privacy assumes a decentralized enough network. Sadly this is not the case with lightning-BTC as most lightning traffic goes through the big Zeus/Phoenix/Aqua/etc. services AFAIK.
- Bad receiver privacy (because receiver exposes node ID).
- When interfacing lightning-BTC ↔ L1-BTC one is of course inevitably dealing with crappy L1-BTC privacy.
If somehow NPT can offer lightning with even better privacy characteristics than lightning-BTC, yes it’s a true killer app indeed. We’re headed for a 10,000 USD/NPT price 
at least if this feat can be pulled off.