Lost as a dog may be (6)

I believe the answer is:

astray

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'lost' is the definition.
(synonyms)

'as a dog may be' is the wordplay.
'a dog may be' becomes 'tray' (I am not sure about this - if you are sure you should believe this answer much more).
'as'+'tray'='ASTRAY'

Can you help me to learn more?

(Other definitions for astray that I've seen before include "Up the garden path?" , "Off one's route or lost" , "Off target" , "In a lost state" , "Wandering off the track" .)

I've seen this clue in The Globe and Mail, The Irish News and The Guardian.

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