As was mentioned Radial tires can be rotated in a cross pattern with the following exceptions:

If they are directional tires, tires that have arrows showing their rotation direction, they MUST be rotated front to back on the SAME side. Lightning’s come with directional tires and can NOT be crossed rotated.

Directional tires are just that, their thread pattern is in a particular direction to direct water from the front to the back of the tire. If you put the tire rotating in the wrong direction you will essentially be continually pushing water in FRONT of the tire, not a good idea…

The other reason why you can not sometimes do cross direction rotation is some alloy rims are constructed in such a fashion to direct air flow to the brakes. Put them on the wrong side and you no longer get any air flow to your brakes.

Other then that, rotate away…