Make weak argument about Lilith going naked (10)
I believe the answer is:
debilitate
'make weak' is the definition.
(debilitating is a kind of making weak)
'argument about lilith going naked' is the wordplay.
'argument' becomes 'debate' (synonyms).
'about' indicates putting letters inside.
'going naked' says to take the centre (the word stripped of its outside letters).
The middle of 'lilith' is 'ilit'.
'debate' going around 'ilit' is 'DEBILITATE'.
(Other definitions for debilitate that I've seen before include "Make very weak" , "Weaken" .)