Translation:My diet is good; that is why my health is good.
My Comprehensive English Esperanto Dictionary has this example under Then: "If you are Mr. Smith, then I am in the right place." "Se vi estas s-ro Smith, tiam mi estas en la ĝusta loko." This is the same kind of sentence you are asking about. Tial has the meaning of "accordingly, for that reason, therefore, that is why." If those are the meanings you are looking for then you could use tial instead of tiam. Just not here.
Notu: Se mi manĝus pli bone, tiam mi pli sanus. kontraŭ: Se mi manĝus pli bone, tial mi pli sanus. (If I would eat better, then I would be more healthy.) (If I would eat better, therefore I would be more healthy.)
But leaving out the word entirely? I don't think so.
A semicolon is usually used to identify the end of a clause and the beginning of a related series of sub-clauses, those usually indicated by commas, or a single related, but different, sub-clause. Think of a bulleted sentence, without breaking out any actual bullets. Most Americans, and far too few other English speaking people, don't know the proper use of the things, and thus don't realize just how useful they can be - in the right place and time. I blame this on the education system trying to make them more complex than they need to be. The sample sentence does use a semicolon correctly.
I thought about tossing in a joke here wherein I use far too many colons: semicolons; hyphens - ellipses… etc! I couldn't think, however, of how to really make it funny and not snarky.