Crossword Genius

Lie when teacher unexpectedly discovers firework (9-5)

Ross

I believe the answer is:

catherine-wheel

I'm a little stuck... Click here to teach me more about this clue!

'firework' is the definition.
(Catherine wheel is an example)

'lie when teacher unexpectedly' is the wordplay.
'unexpectedly' indicates anagramming the letters.
'lie'+'when'+'teacher'='liewhenteacher'
'liewhenteacher' with letters rearranged gives 'CATHERINE-WHEEL'.

'discovers' is the link.
I am not very happy about this link. It may belong to another bit of the clue.

Can you help me to learn more?

I've seen this clue in The Telegraph.
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