The given definition of lexeme begins with "A Lexeme is a lexical element of a natural language" and the model indeed have a language field.
A more flexible way to represent this information would be to put that in statements like "appears in discourses categorized as being expressed in ${language}". Once again, flexibility of claims could help to render the fact that in such or such discourse, the lexeme is considered endogenous of the surrounding discourse, loan word, an exogenous verbatim quote, and so on.
Thus the "language" might always be inferred, but wouldn't be engraved in the model with a rigidity which doesn't reflect versatility of language practices.
On a side note, the "natural language" term is itself carrying very biased assumption on languages, see this Wikiversity research article for more development on this topic.