Crossword Genius

Waste time on a lost cause as rampant falsehood raged (4,1,4,5)

Ross

I believe the answer is:

flog a dead horse

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'waste time on a lost cause' is the definition.
I don't know anything about this answer so I cannot tell whether this works.

'rampant falsehood raged' is the wordplay.
'rampant' indicates anagramming the letters (I've seen this in other clues).
'falsehood'+'raged'='falsehoodraged'
'falsehoodraged' with letters rearranged gives 'FLOG A DEAD HORSE'.

'as' is the link.

Can you help me to learn more?

(Other definitions for flog a dead horse that I've seen before include "fight to no avail" , "deal with an unscrupulous butcher maybe" , "Pursue a lost cause" , "In vain" , "like one coping with dishonesty?" .)

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