Drink doggedly? (3,2)

I believe the answer is:

lap up

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'drink' is the definition.
(lapping up is a kind of drinking)

I don't understand the remainder of the clue.

(Other definitions for lap up that I've seen before include "Accept with obvious pleasure" , "Relish (with the tongue?)" , "Eagerly enjoy" , "Take in willingly (with the tongue?)" , "Delight" .)

I've seen this clue in the Evening Standard.

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