Crossword Genius

Theres nothing under cover, but one may bathe here (4)

Ross

I believe the answer is:

lido

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

'one may bathe here' is the definition.
Although both the answer and definition are singular nouns, I cannot understand how one could define the other.

'theres nothing under cover' is the wordplay.
I cannot quite understand how this works, but
'nothing' could be 'o' (O resembles 0) and 'o' is found within the answer.
'cover' could be 'lid' (lid is a kind of cover) and 'lid' is found in the answer.
No letters remain.
This explanation may well be incorrect...

'but' acts as a link.

Can you help me to learn more?

(Other definitions for lido that I've seen before include "Outdoor swimming pool" , "Swim here" , "Venetian resort" , "---- di Jesolo, Italian Adriatic resort" , "Aquatic leisure centre" .)

I've seen this clue in The Irish News.
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