Crossword Genius

Well-founded desert isle with lake (8)

Ross

I believe the answer is:

rational

'well-founded' is the definition.
(thesaurus)

'desert isle with lake' is the wordplay.
'desert' becomes 'rat' (ratting is a kind of deserting).
'isle' becomes 'iona' (I've seen this before**).
'with' is a charade indicator (letters next to each other).
'lake' becomes 'l'.
'rat'+'iona'+'l'='RATIONAL'

(Other definitions for rational that I've seen before include "Reasonable - sane" , "Of sound mind -- not a liar (anag)" , "Sensible, based on reason" , "Using logic" , "Based on reason or logic" .)

I've seen this clue in The Telegraph.
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