Regarding Nostr,
If the CDN frontends for your relays were cut at the same time in an attack, the content would still exist on that start9 on your local drive, but your followers wouldn't be able to find it (at least temporarily, depending on how much control you still had over the DNS).

Regarding Lightning,
It depends on the wallet's implementation for privacy.  GetAlby allows Cloudflare (and therefore the US government) to see ALL transactions