Persuade to dine out, maybe, with a bit of luck (6)

I believe the answer is:

induce

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'persuade' is the definition.
(I've seen this before)

I cannot understand how the remainder of the clue works.

(Other definitions for induce that I've seen before include "Bring on by artificial means" , "Persuade or bring on, say birth" , "Bring on, cause to happen" , "Persuade, hasten childbirth" , "Give rise to" .)

I've seen this clue in the Evening Standard.

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