Lady singer out to lunch (4)
I believe the answer is:
gaga
'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" .)