If you are buying and wearing one of the older can light models, which are lead-acid, these are very large and heavy, and if you connect it to your BPW belt, then the right side is your only choice, since your argon bottle will likely hang down at your left.
If you are connecting it to your plate, then again, your argon bottle will likely be on your left, so that leaves the right side of your plate.
When you order a light, or buy one, the supplier will normally ask you whether you plan to mount it on you plate or on your belt. I recommend the belt, because that is easier to reach to turn on and off.
The most modern lithium-ion lights have very small and lite batteries, and so the cannister is about the size of your hand, only narrower. These you can wear on either side, since they do not collide with either your deco bottle(s) nor your argon bottle. And the best place again is on your BPW belt. And since your right side is unincumbered, that is the best place for it, if you have only one. If you have 2, then one on either side works fine, for the lite weight and more compact LIon lights.
If you are not dragging along an argon bottle nor deco bottles, you can wear it on either side. That would likely be for a warm water night dive in the tropics. But most people are in the habit of mounting them on the right, just out of habit.
You can easily change hands with holding the lantern. You won't die and go to hades if you don't constantly hold it in your left hand. I can easily hold onto both my DPV handle and my lantern in my right hand at the same time. You cannot signal this way while riding the DPV, but it is a great relief occasionally, or if you need your left hand free.