Lying out with fleas (5)

I believe the answer is:

false

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'lying' is the definition.
(thesaurus)

'with fleas' is the wordplay.
'fleas' anagrams to 'FALSE'.
Though, I'm not sure how the anagram is indicated.

'out' acts as a link.

Can you help me to learn more?

(Other definitions for false that I've seen before include "Mendacious" , "Not in accordance with fact" , "Wrong" , "Not true" , "Not genuine or real" .)

I've seen this clue in the Sydney Morning Herald.

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