Lull to sleep with this music (4)
I believe the answer is:
rock
This could be a double definition.
'lull' is the first definition.
(thesaurus)
'sleep with this music' is the second definition.
'rock' can be an answer for 'music' (rock is a kind of music). I am not certain of the remainder of the definition.
'to' is the link.
Can you help me to learn more?
(Other definitions for rock that I've seen before include "to soothe baby" , "Edinburgh - -" , "Move side to side" , "solid?" , "Music; diamond" .)