Badly out in the spelling of "lively" (6)
I believe the answer is:
evilly
'badly' is the definition.
(I've seen this in another clue)
'in the spelling of lively' is the wordplay.
'lively' anagrams to 'EVILLY'.
Though, I am not sure how the anagram is indicated.
'out' is the link.
Can you help me to learn more?
(Other definitions for evilly that I've seen before include "In wicked or depraved way" , "Extremely wickedly" , "In a very wicked manner" , "in a bad way" , "With wicked intent" .)