Idle though not at first inadequate (7)

I believe the answer is:
lacking
'inadequate' is the definition.
(similar in meaning)
'idle though not at first' is the wordplay.
I cannot quite see how this works, but
'at' could be 'in' (synonymous in some cases - eg at school, in school) and 'in' is found within the answer.
'first' could be 'a' (first letter of the alphabet) and 'a' is located in the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for lacking that I've seen before include "Being without, wanting" , "Absent, deficient" , "'Deficient, wanting (7)'" , "Missing" , "Short" .)