Fast food shop invested in oriental sauce (7)
I believe the answer is:
solidly
'fast' is the definition.
(thesaurus)
'food shop invested in oriental sauce' is the wordplay.
'food shop' becomes 'lidl' (I can't explain this - if you can you should give a lot more credence to this answer).
'invested in' is an insertion indicator.
'oriental sauce' becomes 'soy' (I've seen this in another clue).
'lidl' put into 'soy' is 'SOLIDLY'.
Can you help me to learn more?
(Other definitions for solidly that I've seen before include "with substance" , "Reliably, firmly" , "Working in a financially sound way" .)