"You get mad at the littlest things. You asked for a redwood two by four and I got you one. How was I supposed to know that you didn't want any knots in it? You didn't tell me to pick one out with no knots in it. I wouldn't have agreed to pick one up at all if I had known that you were going to lay an egg about the one I chose," Nina said to Phil.

Is this a correct way to use the idiom? lay an egg about something?

...you were going to (complain my failures) about the one I chose.....??

lay a egg means:

complete failure; [for someone] to do something bad or poorly; to perform poorly on stage.

as in: I just made a huge mistake there; I laid an egg.

But in the above sentence context, I understand what she meant, but is that a legitmate way to use the idiom?

It's not common, no. I'd have to guess at the meaning from the context.

I agree with Clive.
Perhaps you want, "Have a cow!"; "Have a bird!"

My understanding of "lay an egg" is when you present a "completed work" (as the hen does), and it turns out to be worthless, if not rediculous.

I think your author has made a mistake.

- A.