The answer to this is the same reason why people tell you to bring your pinkies together (rotating your wrist) when you do DB flyes. Whether this activates more muscles is yet to really be proven but the idea of it sounds okay.
You need to examine the musculature your working.
A pronated grip for bent over laterals would mean that instaed of your palms facing eachother (neutral grip), your palsm would be facing backwards (when you are bent over or towars the floor when you are standing up. thumb would be pointing down to the floor at the top of the rep). Basically what this is is internal rotation at the shoulder joint. If you were to perform the exercise with a supinated grip (palm facing forward or palm facing the cieling if you are standing. thumbd would be pointed towards the ceiling at the top of the rep), this would be external rotation at the shoulder, and would produce a differnete effect.
So look at the musculature. You are working your rear delts. The basic movement is that you are working your rear delts in horizontal extension (a horizontal movement). Now, by altering whether you are in internal, external or neutral position at the shoulder will alter the way in which the muscle works. Obviously neutral is just that.....neutral, inbetween external and internal. If you were to pronate your hands *external rotation) for the exercises then you are now doing the opposite movement that the rear delt does for the shoulder. The rear delt is an external rotator so doing the opposite of external rotation, which is internal rotation (prontating) this is going to stretch the rear delts (the opposite way a muscle contracts is how you stretch it). So you are asking your rear delts to contract in a stretched state. The final way, my personal favorite, is to do the exercise with a supinated grip. This would put the shuolder in external rotation for the movement. The rear delt is an exeternal rotator so you are now contracting it to its maximum capability (horizontal extensions AND external rotation). It is much harder this way.
the best thing i could tell you is try alll three and vary them up week to week or every few weeks.