At home, lust turned out to be slight (6)
I believe the answer is:
insult
'be slight' is the definition.
(to slight someone is to insult or disrespect them)
'at home lust turned out' is the wordplay.
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'turned out' indicates anagramming the letters (turn out can mean to organise).
'lust' is an anagram of 'sult'.
'in'+'sult'='INSULT'
'to' is the link.
(Other definitions for insult that I've seen before include "Slight - affront" , "Remark intended to hurt or humiliate" , "Hurtful and offensive remark" , "Affront, offend" , "Cause offence to" .)