Made it up for Lawrence to muse (8)
I believe the answer is:
meditate
'muse' is the definition.
('meditate' can be a synonym of 'muse')
'made it up for lawrence' is the wordplay.
'up' is an anagram indicator.
'for' is a charade indicator (letters next to each other).
'lawrence' becomes 'te' (TE Lawrence, Lawrence of Arabia).
'made'+'it'='madeit'
'madeit' with letters rearranged gives 'medita'.
'medita'+'te'='MEDITATE'
'to' is the link.
(Other definitions for meditate that I've seen before include "Consider thoughtfully" , "Think intently and at length" , "Reflect upon" , "Think deeply and quietly" , "Think contemplatively" .)