Crossword Genius

One found in lake regularly lays flat (4,3)

Ross

I believe the answer is:

lily pad

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'one found in lake regularly lays flat' is the definition.
I can't tell whether this definition defines the answer.

'one found in lake regularly lays flat' is the wordplay.
'one' becomes 'I' (Roman numeral).
'found in' indicates putting letters inside.
'lake' becomes 'L' (geographical abbreviation).
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
'flat' becomes 'pad' (a person's home).
The alternating letters of 'lays' are 'ly'.
'l'+'ly'='lly'
'i' going within 'lly' is 'lily'.
'lily'+'pad'='LILY PAD'

Can you help me to learn more?

(Other definitions for lily pad that I've seen before include "Pond feature upon which a frog may sit" , "Frog's floating support?" , "Frog's perch in lake" , "Water feature of floating leaves" , "Frog's floating home?" .)

I've seen this clue in The Times and The Sunday Times.
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