Crossword Genius

Thrill produced by bird, one by lake after dusk? (9)

Ross

I believe the answer is:

titillate

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

'thrill' is the definition.
(I've seen this before)

'by bird one by lake after dusk?' is the wordplay.
I cannot quite see how this works, but
'by' could be 'at' and 'at' is found in the answer.
'bird' could be 'tit' (tit is a kind of bird) and 'tit' is present in the answer.
'one' could be 'i' (Roman numeral) and 'i' is located in the answer.
'lake' could be 'l' (geographical abbreviation) and 'l' is present in the answer.
This explanation may well be incorrect...

'produced' is the link.

Can you help me to learn more?

(Other definitions for titillate that I've seen before include "Thrill" , "create superficial interest" , "Arouse mildly (with images)" , "Excite erotically" , "Stimulate agreeably" .)

I've seen this clue in The Guardian.
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