I like the idea of having some funds involved, to reduce spam, but it will also dramatically reduce adoption. Also, mints are centralized.
About the Lightning idea-- that seems to make sense. Messages can be sent as encrypted notes inside an invoice (which doesn't need to be paid). A whole client could be built for DM over lightning, right? A new lightning address can be spun up and randomA@lightning.com can send "invoices" back and forth to randomB@lightning.com.
Or does it need to be done over Nostr relays for some reason? Or is this an "abuse" of lightning?