The most common and most likely answer to this crossword clue is the 9 letter word ANTEATERS
I've seen this crossword clue in The Guardian
A
N
T
E
A
T
E
R
S
Buddy explains!
The straight part
We know that "they’d like to have lunch with workers" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case they’d like to have lunch with workers = anteaters.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does ANTEATERS mean?
ANTEATERS noun- Any of several animals, in suborder Vermilingua, which are noted for eating ants and termites which they catch with their long sticky tongues.
- Any of some other unrelated species that feed with ants, including pangolin (scaly anteater), echidna (spiny anteater), aardvark and numbat (banded anteater).