Gonzales Digital Image Processing and the Laplacian Operator
Isotropic operator is an operator that has no bias to any particular direction in the image. 
If you see the below Laplacian mask, Edge detection is taking place in every direction.


If you see the below image, three filter kernels are applied. The first kernel detects edges in x direction, the second in y direction and the third is Laplacian kernel detecting edges in all directions, hence it is isotropic.