In lecture, a reason for being stern (4)
I believe the answer is:
rear
'being stern' is the definition.
(rear of a ship)
'in lecture a reason' is the wordplay.
'in' indicates a hidden word.
'REAR' can be found hidden inside 'lecture a reason'.
'for' acts as a link.
(Other definitions for rear that I've seen before include "Jump" , "parent" , "Of horse, rise up on hind legs" , "Hind part" , "what you may bring up" .)