Imagine embodying casual lilt of the unimpeachable (9)

I believe the answer is:

guiltless

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

'unimpeachable' is the definition.
(similar in meaning)

'imagine embodying casual lilt of' is the wordplay.
I cannot quite see how this works, but
an anagram of 'lilt' is 'iltl' which is located in the answer.
'imagine' could be 'guess' (synonyms) and 'guess' is present in the remaining letters.
No letters remain.
This may be the basis of the clue (or it may be nonsense).

'the' acts as a link.

Can you help me to learn more?

(Another definition for guiltless that I've seen is " Innocent".)

I've seen this clue in the Sydney Morning Herald.

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