Thoroughly chaotic in Lidl, get close to apoplexy (10)
I believe the answer is:
diligently
'thoroughly' is the definition.
(thesaurus)
'chaotic in lidl get close to apoplexy' is the wordplay.
'chaotic' indicates an anagram.
'close to' suggests the final letters (the close/ending of).
The final letter of 'apoplexy' is 'y'.
'in'+'lidl'+'get'='inlidlget'
'inlidlget' anagrammed gives 'diligentl'.
'diligentl'+'y'='DILIGENTLY'
(Other definitions for diligently that I've seen before include "With meticulous care" , "with application" .)