After sending a DM, the profile lacks access to it. I can see my posts and public comments, but not my DMs. Thus there is also no way to read or edit DMs Lemmy users have sent.

update

As @viking@infosec.pub points out, sent messages are accessible in the ALL tab. Once my DMs are rendered, indeed there is an option to edit them just like a public message. But presumably due to another bug, Lemmy recipients are not likely notified of edits (untested).