Concerning the kitchen Lucy and I ran badly (8)
I believe the answer is:
culinary
'concerning the kitchen' is the definition.
(culinary means relating to food or cooking)
'lucy and i ran badly' is the wordplay.
'and' says to put letters next to each other.
'badly' is an anagram indicator.
'i'+'ran'='iran'
'lucy' after 'iran' is 'iranlucy'.
'iranlucy' with letters rearranged gives 'CULINARY'.
(Other definitions for culinary that I've seen before include "Relating to cooking" , "Relating to cookery" , "To do with or used in cooking" .)