Bird, one repeatedly around Lake (8)

I believe the answer is:

titicaca

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

'bird one repeatedly' is the wordplay.
'bird' becomes 'tit' (tit is a kind of bird).
'one' becomes 'i' (Roman numeral).
'repeatedly' becomes 'caca' (I can't justify this - if you can you should give a lot more credence to this answer).
'tit'+'i'+'caca'='TITICACA'

'around' is the link.

Can you help me to learn more?

(Other definitions for titicaca that I've seen before include "Large lake on the Peru-Bolivia border" , "high water" , "Large Andean lake" , "Large lake bordering on Peru and Bolivia" , "high lake" .)

I've seen this clue in The Guardian.

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