Mine did the same: again, she had a chronic health problem, also severe anxiety. (no learning difficulties though) Stopped around the age of 10.
I seemed to spend a lot of time restraining her and repeating again and again: "No, I cannot let you hurt anyone, no, I am not going to let you hurt anyone." Later on she did become suicidal.
But she is now grown up: she is living independently and is getting on fine training for a demanding career. She is on anti-depressants and will probably stay on them for the foreseeable future but that is ok as long as she is ok.
I did not punish after the event: I got the impression she hardly knew what she was doing during a meltdown and she has later confirmed that she couldn't really even recognise people when she was at her worst: it felt like some hideous monster was attacking her and she had to defend herself. So it didn't seem fair to punish any more than I would have punished for lashing out in a delirium. (incidentally, she gets delirious really quickly with even a slight fever)
I grew up with a sibling doing very much the same, though they are not biologically related: in his case, it was almost certainly adoption trauma. Again, came to an end around the age of 10- after the time when he nearly laid our father out cold. And he has grown up into a very lovely adult with absolutely no problems re violence.