Tool, visibly sore, covered in soap (8)
I believe the answer is:
Here is my best explanation:
'covered in soap' is the definition.
'tool visibly sore' is the subsidiary indication.
'tool' becomes 'lathe'.
'visibly sore' becomes 'red'.
(Other definitions for lathered that I've seen before include "Created a froth" and "Soaped as for shaving".)