What's the difference between lexeme and lexical item?

Question

While studying An Introduction to English Morphology by Andrew Carstairs-McCarthy, came across this fragment.

Section 2.1 pointed out that we tend to think of words as possessing two characteristics: 1. they have meanings that are unpredictable and so must be listed in dictionaries, and 2. they are the building-blocks for words and phrases. In Sections 2.3 and 2.4 I have argued that, although this may be broadly true, the two characteristics do not always go together. For this reason, it will be helpful to have distinct terms for items with each of the two characteristics. Let us use lexical item for items with characteristic 1., and reserve word for items with characteristic 2.

Can anyone explain what's the difference between those terms? It seems to me lexeme is an abstract entity sometimes called ‘dictionary word’, but lexical item appears to be that same concept.

Answer 1

A lexeme is an abstract concept that represents the core meaning shared by a set of closely-related word-forms (e.g. the concept of 'live' is the lexeme for the word-forms 'lives', 'live', and 'lived').

Lexemes are abstract concepts without phonological forms; so the word 'live' is not a lexeme, but the abstract concept of 'live' is. To make this distinction, lexemes are typically represented by writing its lemma (i.e. dictionary or citation form) in small caps, like this: ʟɪᴠᴇ.

A lexical item, lexical unit, or lexical entry is any concrete item listed in the lexicon. It can be a single word (e.g. 'cat') or a phrase (e.g. 'rabbit hole').