I do not know what the ideal depth and spacing of the grooves should be. But, I can describe the grooves in my lapping plate. My plate has grooves that are approximately 2 mm wide by about 2 mm deep. They are spaced about 10 mm between grooves. The two sets of lines are not at a 90 degree angle. They are at about a 60 degree angle. So, the small lands formed by the grooves diamond shaped with the points of the diamond having and angle of about 60 degrees and the sides of the diamond having an angle of about 120 degrees.
When I answered the original question, I was not expecting you to construct a lapping plate from scratch. They can be purchased as a complete unit, ready to use. But if you are determined to make your own, this pattern should work.
Johnny Pellin