Kind of prayer enlightened unspecified number (6)
I believe the answer is:
litany
'kind of prayer' is the definition.
'enlightened unspecified number' is the wordplay.
'enlightened' becomes 'lit' (I've seen this before).
'unspecified number' becomes 'any' (I've seen this in another clue).
'lit'+'any'='LITANY'
(Other definitions for litany that I've seen before include "Form of church prayer" , "Repeated prayers" , "Long and tedious series" , "part of service" , "Long list (of requests or complaints)" .)