Condition of lush sauces by Arab American (10)
I believe the answer is:
dipsomania
'condition of lush' is the definition.
(a lush is an alcoholic)
'sauces by arab american' is the wordplay.
'sauces' becomes 'dips'.
'by' says to put letters next to each other.
'arab' becomes 'omani' (Omani is an example**).
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'dips'+'omani'+'a'='DIPSOMANIA'
(Other definitions for dipsomania that I've seen before include "Having huge thirst" , "Compulsive desire for alcohol" , "Alcoholism - so dim a pain (anag)" , "Problem for lush" , "Boozer's compulsion" .)