Using patterns in addition/instead of background colors in lattice plots

Question

I am using level plots from the R lattice package. My resulting plots look like the one shown below.

My problem now is that I need to generate a black and white version for printing.

Is there a way to change the colors to grayscale and give the rectangles a background pattern so the the red once are distinguishable from the blue ones? For example, dots or diagonal dashes come to mind.

Thanks!