Lesson starting late means test! (4)
I believe the answer is:
oral
'test' is the definition.
(I've seen this before)
'lesson starting late' is the wordplay.
'lesson' becomes 'moral' ('moral' can be a synonym of 'lesson').
'starting late' means to remove the first letter (the word starts later than the beginning).
'moral' with its first letter taken away is 'ORAL'.
'means' is the link.
(Other definitions for oral that I've seen before include "Vocal test" , "Related to the mouth" , "By word of mouth, like some exams" , "Spoken test" , "Relating to speech" .)