Well-read story entertains time after time after time (8)

I believe the answer is:

literate

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'well-read' is the definition.
(synonyms)

'story entertains time after time after time' is the wordplay.
'story' becomes 'lie' (story can mean a fabrication).
'entertains' indicates putting letters inside.
'time' becomes 't' (abbreviation).
'after' says to put letters next to each other.
'time after time' becomes 'rate' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'lie' placed around 't' is 'lite'.
'lite'+'rate'='LITERATE'

Can you help me to learn more?

(Other definitions for literate that I've seen before include "Learned" , "version of 'speed of light'?" , "Erudite" , "Well-read" , "Scholarly" .)

I've seen this clue in The Independent.

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