An "idiomatic expression" is an idiom. This means that the whole expression does not logically mean what the combination of each of the words means.
"¢ Here is the definition of "idiom" from The American Heritage Dictionary*:
idiom, a phrase or grammatical construction that cannot be translated literally into another language because its meaning is not equivalent to that of its component words. Common examples, of which there are thousands in English, include follow suit, hell for leather, flat broke, on the wagon, well hung, etc. By extension, the term is sometimes applied more loosely to any style or manner of writing that is characteristic of a particular group or movement.
"¢ Here is the definition of idiom from: The New Dictionary of Cultural Literacy**
A traditional way of saying something. Often an idiom, such as "under the weather," does not seem to make sense if taken literally. Someone unfamiliar with English idioms would probably not understand that to be "under the weather" is to be sick.
"¢ Here is the definition of "idiomatic expression" from WordNet***
The noun idiomatic expression has one meaning:
Meaning #1: an expression whose meanings cannot be inferred from the meanings of the words that make it up
Synonyms: idiom, phrasal idiom, set phrase, phrase
The phrases you are asking about -- have lunch, have time, keep fit – what do you want the Grammar Exchange to do with them?
Some of the word combinations like these are not normally listed in books or collections of idioms. They might be listed in books or collections of phrasal verbs, or in books or collections of "collocations," which can be defined as any usual grouping of words.
"Have lunch," for example, is listed in the Oxford Collocations Dictionary for Students of English*** under "meal." There you will find different verbs that go with different meals. For example, under "eat, have, take" you see: "Have you had breakfast?"
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*The American Heritage Dictionary of the English Language, Fourth Editition. Houghton Mifflin Company. 2007
**The New Dictionary of Cultural Literacy, Third Edition Edited by E.D. Hirsch, Jr., Joseph F. Kett, and James Trefil. Houghton Mifflin Company. 2002
***WordNet 1.7.1 Copyright © 2001 by Princeton University.