Phonemes are realized through phones, morphemes are realized with morphs. What is the corresponding word for a lexeme? A casual google search isn't telling me much.
LEXICAL ITEM, depending on your framework) is, indeed, what you have in mind (the emic unit) then
LEX could be its counterpart (the etic unit), with the other realizations being its
ALLOLEXES (as pointed out by curiousdannii). Nevertheless, I have seldom seen either of the two terms used in English: you will find them neither in Trask's Dictionary of Grammatical Terms (1996), for example, nor in Crystal's The Cambridge Encyclopedia of Language (1997, second edition) or his A Dictionary of Linguistics and Phonetics (2008, sixth edition) or Strazny's Encyclopedia of Linguistics (2005) or Malmkjær's The Routledge Linguistics Encyclopedia (2010, third edition), and you will find merely a single mention of allolex in Collinge's An Encyclopaedia of Language (2005) and just a few more in Brown's The Encyclopedia of Language and Linguistics (2005, second edition), although their equivalents certainly do occur, for example, in German and Czech linguistic texts more frequently as far as I am aware.
An example of terminological divergence, probably stemming from different linguistic tradition/framework, can be seen in the following quotation from an article by Joachim Mugdan of the University of Münster, Germany, Units of word-formation (currently in press, available here as a PDF manuscript (p. 19, all emphasis mine):
A lexeme is a set of grammatical words which have the same content, save for their morphosyntactic properties. While grammatical words are linguistic signs, a characterization of lexemes as signs (cf. Aronoff 1994: 9; Montermini 2010: 86) deprives this term of its meaning. Occasionally, a grammatical word is called lex or, in relation to the lexeme it belongs to, allolex (in analogy to allomorph, see section 2.3.).
Although the term
grammatical word has sometimes been used instead, I find it rather confusing, because it can also refer to words having a grammatical function (i.e. function words) rather than lexical content (i.e. content words). I myself prefer the term
morphological word, or rather
MORPHOSYNTACTIC WORD, to emphasize its syntactic/syntagmatic dimension, as opposed to the concepts of
phonological word and
orthographical word, with which it can, but does not have to, coincide in different languages. Nonetheless, I would definitely recommend the term
WORD-FORM, suggested by jlawler and Alex B. in their comments, as it appears to be far more frequent in the literature and is thus preferable.
Inscription I'd generally say. You ask for a surface name, so it depends which surface: on the phonological surface, there's these inscriptions or morphemes, which then go to become phones as you said. On the other, the meaning surface, the inscriptions are interpreted as morphemes or morphemes' features, I guess.