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In the French "A-t-il soif ?" there are several (inflected) lexemes ("A", "il", "soif"), and an empty morph "t".

The morph "t" has no meaning which is why it's an empty morph; it's there purely for the purpose of euphony.

Is an empty morph such as "t" also considered a lexeme? If not, is there a super group that includes both morph(eme)s and lexemes?

I don't think there is a theory-neutral term for the "super group" you're looking for—and I think the reason there isn't is that no such term would help the way you want it to.

Pre-theoretically, I don't think there's a problem. Presumably French people just think they're putting the words "a", "t", and "il" together, right? It's only when you try to rigorously define what they mean in some theoretical framework that "hold on, 't' has no semantics, so it can't be the same kind of thing as 'a'" even comes up.

In most definitions, morphemes are just the indecomposable parts of lexemes. But what are lexemes? That's the tricky part.

• In many theories, it's not a problem for lexical entries to have null semantics—"it" in "it's raining" is pleonastic, but still a lexeme, and there's no reason "-t-" in your example couldn't be the same. (Of course "-t-" is also the sole morpheme in that lexeme, but you don't need your super group here.)


• In other theories, lexemes have to have semantics, so what you actually have is a whole bunch of separate lexemes that have all have that "-t-" in the middle, which are "produced in the lexicon".¹
  
  
  • Sometimes that just means that it's part of morphosyntax rather than phrase syntax, so there is clearly a "-t-" morpheme that all of those lexemes can be built from on the fly. So here, but really only here, your proposed super group would be useful.
  
  
  • In other versions (including the original sketch by Chomsky), if "-t-" isn't in the lexicon, it isn't being used by morphosyntax. There is no such thing as a "-t-" morpheme,² or any "-t-" thing anywhere in the language, so no super group could help here.
  
  
  
  


• Many theories that reject "-t-" as a lexeme aren't doing so because it has no semantics, but because (they claim) it has no independent existence.³
  
  
  • In a Steven Pinker-inspired "words vs. rules" treatment, what you have is a euphony rule—which lives in your "rules engine database", not your "lexicon"—that inserts the /t/ phoneme without having to grab anything out of the lexicon. There is no "-t-" lexeme, and no "-t-" morpheme, anywhere in the language. I don't know of a good word for "phoneme clusters embedded in rules", but they're definitely not morphemes, and there's no supergroup that will include them and lexemes together.
  
  
  • In a constructional approach, instead of a "euphony rule" stored in a separate rules engine, you have a construction (or family of constructions) stored in the lexicon, right alongside the words. For example, in Peter Culicover and Ray Jackendoff's Parallel Architecture, there's no lexeme "-t-", but there is a lexical entry we can call "euphonic α-t-β", a construction which includes phonological and syntactic information and interface constraints⁴ but nothing semantic⁵. Could you call "-t-" a morpheme in their treatment? Maybe,⁶ but even if you can, I think it misleads more than it helps to try to talk about morphemes and simple lexical entries as a group, rather than constructional and simple lexical entries as a group.
  
  
  
  

There are probably other theoretical approaches to morphosyntax that I haven't covered here, but that should be enough to explain why there's probably no term that applies to all of them that gives you what you want.

_{1. I'm taking your analysis for granted here. I think if pressed, most people who supported this kind of theory would insist that there must actually be some semantics for "-t-" so it can be a lexeme, to avoid this conclusion.}

_{2. Of course you could still call "-t-" a morpheme in the diachronic history of each of the separate lexemes that uses it. But it isn't a morpheme in the language as a language, so that's more misleading than helpful. And the same goes for some of the other treatments below, including the next one.}

_{3. Although they may use the fact that it has no semantics to argue that it must not be an independent lexeme, that's at the metatheoretical level.}

_{4. There's the /t/ sound, probably some prosody information, the linear ordering, both euphonic and morphosyntactic constraints on what can be inserted in the two variable slots…}

_{5. This is badly oversimplified, more like Culicover's earlier treatment than like actual PA, but it gets the idea across.}

_{6. Any good instantiation of their system (which hopefully includes the human brain) is surely going to use (both regular and quasiregular) commonalities to optimize storage and lookup of different constructions that, e.g., all stick a /t/ in the middle. So there could be a generic "-t-" that "euphonic α-t-β" inherits from, which you could easily call "the '-t-' morpheme". But there could just as well be some kind of implicit associative analogy storage that doesn't have anything you could point to as "the '-t-' morpheme".}