Lemmy offers the option to link a Matrix account to your Lemmy account. On the web interface, every Lemmy account to have done so shows a "Send encrypted message" button that directly links to that Matrix account.

Could such a button also be integrated into the Eternity app?

For those who don't know, direct messages on Lemmy aren't encrypted. They are, I think, exchanged via the ActivityPub protocol which doesn't provide for encrypted communication.

Matrix is a different federated, open source protocol, designed for encrypted direct messaging and encrypted group chats. It's a bit like Discord, but federated and open source. You can create an account for example on element.io which offers both a web interface and downloadable apps for most operating systems.