Legendary figure to go brown: Greek character around lake getting sun (8)
I believe the answer is:
tantalus
'legendary figure' is the definition.
(figure in Greek mythology)
'go brown greek character around lake getting sun' is the wordplay.
'go brown' becomes 'tan' (get a suntan).
'greek character' becomes 'eta' (letter from the Greek alphabet).
'around' says to take the centre.
'lake getting' becomes 'alu' (I am not sure about this - if you are sure you should believe this answer much more).
'sun' becomes 'S' (abbreviation).
The central letter of 'eta' is 't'.
'tan'+'t'+'alu'+'s'='TANTALUS'
'to' is the link.
(Other definitions for tantalus that I've seen before include "Secure liquor decanter" , "Frustrated Greek" , "Son of Zeus and case for decanters" , "Lydian king" , "Lockable case for decanters" .)