When I bought my Celeb III around 1970 it had the original case. It's no longer with us today. Lets just say they were not the best even at that time. So you probably don't want an original.
A Celeb III body fits tight in a ES335 case, but it usually fits. The problem can be the neck support. In some cases the neck in the nut area sits too high to close the case and angles the body a bit so it may look like its low at the bottom.
Here is my experience. Mine will not fit a 1980's Gibson USA case (neck sits too high). Mine will just barely fit a 1962 Lifton for a ES 335. It fits fine in a stock Shearaton case probably made in Korea.
It's best to actually take it to a music store and check the fit. My guitars current home turned out to be a TKL (Canada). The
construction is pretty good, the price was reasonable and the fit is perfect. BUT be aware. The new cases from Canada off gas when they are new and your old finish my not like that. If you get a new case, I'd put it out in the sun for a few days.


Note: you don't say celeb I / II / III. If you have a I your going to require a deeper case but the take it in and check it rule still applies.
Rich