Altered lie by misbehaving on purpose (12)
I believe the answer is:
deliberately
'on purpose' is the definition.
(synonyms)
'altered lie by misbehaving' is the wordplay.
'misbehaving' indicates an anagram.
'altered'+'lie'+'by'='alteredlieby'
'alteredlieby' anagrammed gives 'DELIBERATELY'.
(Other definitions for deliberately that I've seen before include "as intended" , "On purpose" , "Consciously and intentionally" .)