Left order for piece of liver (4)

I believe the answer is:

lobe

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'piece of liver' is the definition.
'lobe' can be an answer for 'piece' (lobe is a kind of piece). I'm unsure of the 'of liver' bit.

'left order' is the wordplay.
'left' becomes 'L' (common abbreviation).
'order' becomes 'obe' (Order of the British Empire award).
'l'+'obe'='LOBE'

'for' acts as a link.

Can you help me to learn more?

(Other definitions for lobe that I've seen before include "part of brain" , "Base of ear" , "Bottom part of ear" , "Leaf division" , "Part of ear or leaf" .)

I've seen this clue in the Sydney Morning Herald.

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