Crossword Genius

Lady singer out to lunch (4)

Ross

I believe the answer is:

gaga

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'lady singer' is the definition.
(Lady Gaga the singer)

I don't understand the rest of the clue.

Can you help me to learn more?

(Other definitions for gaga that I've seen before include "Slangily crazy, off one's head" , "Bats" , "Lady who sings" , "bananas" , "Lady < > in a senile" .)

I've seen this clue in The Independent.
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