Lag engages posh doctor over complaint (7)

I believe the answer is:

lumbago

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

I don't understand the remainder of the clue.

(Other definitions for lumbago that I've seen before include "Back problem" , "Gaul mob (anag.)" , "Rheumatism of lower back" , "Rheumatic pain in muscles of lower back" , "Maul bog badly for a rheumatic affliction" .)

I've seen this clue in The Sun.

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