The texts that I have say that you get grating lobes when spacing exceeds 1 wavelength*. You can look at it this way, consider a simple driven array of two identical elements, which is the simplest array. When the spacing is less than 1 wavelength, it is impossible to find a direction beyond a single line through the array where there is complete constructive interference. For example, if the two elements are driven in-phase, the only direction in which their emissions add together perfectly in phase is broadside in a single line perpendicular to the plane of the elements. In all other directions, the emission from the two antennas do not combine perfectly in phase. Now, imagine that you increase the element spacing to 1 wavelength. Now, you can imagine that you will get perfect in-phase combination not only broadside to the array, but also on a line through the two elements as well. This must be so because we have spaced them one wavelength apart so emission from one element will be back in phase when it propagates to the other element and the total emission continueing in that direction will remain in phase from both elements.
As spacing goes beyond 1 wavelength, the direction in which you get in phase combination starts to move away from the axis through the two elements and when spacing reaches two wavelengths, you get a new grating lobe on that axis again for a total of 3 axes where there is perfect combination.
* ref: Kraus "Antennas For All Applications", 3rd Edition, page 598