I have experience with this. What wired mode does is simply uses the Ethernet channel over thunderbolt. So it’s just like what you would expect if you‘re connecting a computer to the internet using wired vs Wi-Fi. That is, lag isn’t eliminated, but it’s usually more consistent since there is typically less signal degradation and interference from the environment. If you have a really good Wi-Fi setup, the difference in either case isn’t very noticeable.
The lag introduced from Luna is due to the fact it has to compress a fairly complex video stream on one machine while also having to decompress it in on another and do it all in real-time. They’ve done some truly impressive work to pull this off, but at the end of the day it will never be quite like a direct connection/target display mode.