Lying back looking lethargic (6)

I believe the answer is:

supine

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This could be a double definition.

'lying back looking' is the first definition.
'supine' can be an answer for 'lying' (I've seen this before). I am not sure about the 'back looking' bit.

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

Can you help me to learn more?

(Other definitions for supine that I've seen before include "Lying face upward" , "Lying on one's back - passive" , "Use pin (anag.)" , "looking up" , "Prostrate" .)

I've seen this clue in the Evening Standard.

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