That didn't take long - the LG V20 has already been rooted
The root solution comes by way of various XDA users, and the method that's been found involves installing TWRP on the device and then using that to flash SuperSU. As always, rooting comes with a bit of risk and does void the V20's warranty. With that being said though, the solution here looks to be fairly fool-proof and some users are already commenting about their success over on the XDA forums.
LG's V20 boasts a massive 5.7-inch 2K display, dual 16MP and 8MP rear-facing cameras, 4GB of RAM, Snapdragon 820 processor, 3200 mAh battery, high-quality DAC, and Android 7.0 Nougat. It certainly has all of the high-end features you could ask for in a flagship Android phone, but with LG's custom UI never being a strong point for their devices, rooting the V20 and tweaking the interface's appearance could turn it into a nearly perfect handset.
If you're interested in rooting the V20 for yourself, all of the instructions can be found here.