Very slim coat for Luke given a comfortable place (7)

I believe the answer is:

leanest

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'very slim' is the definition.
I can't tell whether this defines the answer.

'coat for luke given a comfortable place' is the wordplay.
'coat for' suggests removing the centre (the letters which coat the word).
'given' means one lot of letters go next to another.
'comfortable place' becomes 'nest' (I've seen this in another clue).
'luke' with its centre removed is 'le'.
'le'+'a'+'nest'='LEANEST'

Can you help me to learn more?

(Other definitions for leanest that I've seen before include "Least fatty" , "Most skinny" , "Most thin" , "Poorest-quality" , "Most unproductive" .)

I've seen this clue in The Guardian.

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