Lakes surrounding isle with cooler shade (5)

I believe the answer is:

lilac

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'shade' is the definition.
(lilac is a shade of purple)

'lakes surrounding isle with cooler' is the wordplay.
'lakes' becomes 'LL' (a geographical abbreviation for lake written twice).
'surrounding' is an insertion indicator.
'isle' becomes 'i' (geographical abbreviation).
'with' says to put letters next to each other.
'cooler' becomes 'ac' (I can't justify this - if you can you should believe this answer much more).
'll' placed around 'i' is 'lil'.
'lil'+'ac'='LILAC'

Can you help me to learn more?

(Other definitions for lilac that I've seen before include "Flowering tree of the olive family" , "Drop by about one, turning" , "Tree - pinkish-purple colour" , "Mauve-like colour" , "Fragrant,purple flower" .)

I've seen this clue in The Times.

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