Upgrading the firmware of your lens is the same way as you were upgrading your camera’s firmware where you just need to download the newest version of the firmware for your lenses, put it on a clean memory card, and then place it in your camera and run it.
But some third-party lenses have slight differences. You can update it by using utility software and some hardware component that is for separate purchase or it may be provided by the manufacturer when you purchase the lens. Your lens will be connected to the computer via a connector port then it goes through the same procedure in updating your camera firmware. You can follow the procedure mentioned above.