A few weeks ago, the topic came up and I commented on Beehaw: https://beehaw.org/comment/361658
Given the beta status of Lemmy, I don't even think it's a great idea to give the appearance of privacy. I think the core purpose of a webapp like Lemmy is public messages.
I think it's a can of worms for server operators to get into the business of thinking they can safely hold private messages between users/strangers. None of the Lemmy instances I've joined have had a "terms of service" or anything like that on SIgn Up, I really think the message should be sent far and wide that Lemmy is about posting IN PUBLIC and that messages are being FEDERATED to peers, even people that you don't know could be collecting the data for a search engine.
With small-time server operators opening up hundreds of Lemmy instances, without giving away their experience or human identity, how can you have any confidence that someone is properly securing a server they only have part-time job to update and operate? Major corporations are having their database stolen, Valve, Sony, Nintendo, health care companies, mobile network companies (AT&T)... you think a low-budget shoestring server by a hobbyist running Lemmy should be held to the same standards as a corporation who has an entire team and services to defend their data?
EDIT: Same goes for putting your Lemmy password into a smartphone app or other third-party client. Why should Lemmy server operators be claiming privacy when you have no idea (and no agreement with) who is front-ending your API? You have a 'man in the middle' right there, with full access to Lemmy logins.