Incessant refusal in Lyon: diners get no soup in the end (3-4)
I believe the answer is:
non-stop
'incessant' is the definition.
'refusal in lyon diners get no soup in the end' is the wordplay.
'refusal in lyon' becomes 'non' ('no' in French).
'in the end' says to take the final letters.
The last letters of 'diners get no soup' are 'stop'.
'non'+'stop'='NON-STOP'
(Other definitions for non-stop that I've seen before include "Going straight from A to B" , "continuously" , "Uninterrupted" , "Continuous" , "Unceasing" .)