Greek character lies about breakfast dish (6)
I believe the answer is:
muesli
'breakfast dish' is the definition.
(I've seen this before)
'greek character lies about' is the wordplay.
'greek character' becomes 'mu' (letter from the Greek alphabet).
'about' indicates an anagram.
'lies' is an anagram of 'esli'.
'mu'+'esli'='MUESLI'
(Other definitions for muesli that I've seen before include "Breakfast mixture of oats, nuts, fruit etc" , "Breakfast cereal mix" , "Mixture of cereals etc" , "Swiss breakfast?" , "Breakfast dish with cereals, nuts, fruit etc" .)