What is the meaning of the length of diagonal lines in FFT
If you rotate an image (2D function), its 2D Fourier transform also rotates.

Those lines mean you have something like a barcode oriented in that direction in your image. In one direction it has lots of variations and behaves like a white noise with flat spectrum and in the other direction it has very slow variations.

I'm not sure what do you mean by the length of diagonals, but it's a visual measure of maximum frequency available in those directions.