An Ethernet Lightning adapter will physically connect your iPhone to your home router but downloads may not be faster. Unless you’re paying your ISP for 100Mbit networking or better, the iPhone’s WiFi is not what is limiting download time. The company hosting the videos may not allow the videos to download any faster.
If you have the option to do so, it would probably would be less tedious (but not necessarily faster) to download the videos to a computer then transfer them to the iPhone.