Clear piece of luck for the plain-clothes men (5)

I believe the answer is:

lucid

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'clear' is the definition.
(similar in meaning)

I don't understand how the rest of the clue works.

(Other definitions for lucid that I've seen before include "Clear, sane" , "Clear, easily understandable" , "completely clear" , "Transparent" , "Transparently clear" .)

I've seen this clue in the Evening Standard.

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