Box you might help to pack, thus missing flight? (4)

I believe the answer is:

lift

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'pack thus missing flight?' is the definition.
'lift' can be an answer for 'pack' (thesaurus). I am not sure about the 'thus missing flight?' bit.

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for lift that I've seen before include "Raise - hoist" , "Pick up" , "Raise the vertical conveyor" , "encouragement" , "Free ride" .)

I've seen this clue in The Independent.

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