Lied about store (4)
I believe the answer is:
deli
'store' is the definition.
(I know that deli is a type of store)
'lied about' is the wordplay.
'about' indicates an anagram.
'lied' with letters rearranged gives 'DELI'.
(Other definitions for deli that I've seen before include "Fine food shop" , "food outlet" , "Unusual food shop" , "Shop selling processed food products" , "Food store" .)