In case you missed it, many Android Wear watches are getting WiFi support. Many LG G Watch R owners would love to have that feature enabled on their device. The good news is someone has already pulled that off. Xda-developers user Tasssadar has published a post that shows he it was done. Apparently, the solution works without any issues. You are going to need a G watch R running the 5.1.1 update to get started.
All the instructions are available on Xda-developers. Keep in mind that you could always brick your watch if you are not too careful. The developer suggests WiFi works fine on the watch though.