In a communication between Carla and Ian (original web developer of the first LLResearch.org), Carla wrote:
There is no deeper reason for the spelling of either Latwii or Hatonn than my sense of how the name “sounded” or felt. Latwii sounds like LaTWEE. But the double-e looks a bit goofy compared to Latwii, which is equally easy to sound rightly. Latui is not bad phonetically. Same with Latwi. Somehow, the extra ‘I’ in popped a long time ago and felt right.
As to Hatonn, I originally spelled it Hatton, as that is a place and family name we see in these parts. However it looks like it is pronounced HATon, and the Confederation entity’s name is sounded HatON. To guide people to sound it that way I switched decades ago to Hatonn.“
From this one can extrapolate the cause behind the other spellings.