It’s something that you should worry about. The lens thickness mostly depends on your prescription and the lens index. If you choose the same index, the right side will be thicker.
Actually I have a similar situation to yours. No worries, it won’t be problem. I asked my optician to make the lens on both sides into the same thickness. However, there will be extra charge for the requirement, which is understandable to me.
I think so. My grandfather has -9.00 forthrightness on left eye and -4.00 on the right side. And indeed, his left lens is so much thicker than the other one. Looks quite funny.