Quick to move to correct some of the white lies (5)

I believe the answer is:

lithe

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'quick to move' is the definition.
(I've seen this before)

I don't understand the remainder of the clue.

(Other definitions for lithe that I've seen before include "Supple and graceful" , "Slim and supple" , "Physically supple, agile" , "Not inflexible" , "showing flexibility" .)

I've seen this clue in the Evening Standard.

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