[RHSeeger]

While this is certainly outside my wheelhouse, what I see in various locations is that (at least for English)

- A multi-word phrase is a phrase, not a word

- A lexeme is a basic unit of meaning in a language, like a word (and it's forms [1]) or phrase.

- Every place I was able to find described a lexeme as a "word _OR_ phrase", making it clear those two are different things.

- Dictionaries, in general, focus on words. Many do include phrases also. This point is less definitive; and just my understanding from looking at dictionaries and how they describe themselves. That being said, every source I can find that discussed something close to the topic seems to support this

[1] A word with all it's forms, in that "walk", "walked", and "walks" are all a single lexeme (with each form being a distinct word) OR a phrase

Side note: I'm not looking to "correct" anyone; just pointing out what information I'm able to find on the topic. I'm open to being corrected, but that correction would need to include reasonable sources.

[win311fwg]

While not all phrases are words, the specific phrases we are talking about are a type of word known as an open compound word.

[RHSeeger]

Oh. Thank you for this. I learned a new term today :)