What is the difference? Is lying in state a term reserved for public officials?
Yes. “Lying in state” is a term that means the body is laid out, officially, on a bier so folks can all come and pay their respects during an official viewing period. It doesn’t have to be a government official of some sort–regular folks can sometimes be referred to as “lying in state”, too, but it usually means an official, important person or celebrity of some kind. And usually the “lying in state” period goes on for longer than the few hours that a regular funeral home “viewing” goes on. It’s usually for a period of days.
Lenin has been “lying in state” for about 75 years now.
“Lying in repose” doesn’t mean anything, AFAIK, other than the plain English meaning of “lying down and resting”.
From an AP article on the funeral: