Oddly smooth — and lush! (3)
I believe the answer is:
sot
'lush' is the definition.
(both can mean a drunk)
'oddly smooth' is the wordplay.
'oddly' indicates alternate letters (letters in the odd-numbered positions are used).
The alternating letters of 'smooth' are 'SOT'.
'and' is the link.
(Other definitions for sot that I've seen before include "One's often intoxicated" , "drunk" , "A chronic drinker" , "Habitual drinker" , "One drinks" .)