Yes, the famous brand like louis vuitton sunglasses will have the serial numbers. If you want to check its realness, you could call the sunglasses center to check with the number on the trade mark which is hung at the frame side. After checking with the numbers, you will know whether it is real.
As you know, louis vuitton belongs to the top fashion products sellers which is dedicated to providing a wide range of products including sunglasses to customers from all over the world. They pay a lot of attention to tackle fakes problem. Therefore, you will find serial numbers when you purchase sunglasses from them. And you need to check the numbers with their online systems or personal assistance.