In case of 4chan it's obviously other anonymous imageboards. There doesn't seem to functionality in Lemmy that would allow for posting without accounts.
Not possible really. The protocol Lemmy uses requires accounts, not only as a soft requirement, but the software your instance would be interacting with requires it to function.
It could always use an "anonymous" pseudo-account, (ie, have anonymous posts federate as anonymous@instance.com), or a pseudo-account per post (anonymous1@instance.com, anonymous2, etc). Thinking about it, the former has the advantage of being easy to block by instances or comms that don't like it.
I imagine it wouldn't be hard to add that functionality to an instance, but given the pearl clutching Lemmy instance admins are prone to it would be defed pretty quickly.
It would be defed pretty quickly because all bots, alt right trolls, pedophiles and anyone looking to share illegal content would instantly flock to it.
Sorry you being able to store child porn on my instance is considered pearl clutching. No fucking way I want that responsibility because I like to read memes.
Tell you what: you go host that instance, with no pearl-clutching. Don't worry about any knocks at the door, or federal agents abseiling through your windows. You don't clutch no pearls, right?
My point was more that instance admins defed for things that are comparatively minor, relative to allowing anonymous posting, not that allowing anonymous posting is a good idea (even if it's technically possible).