To try to coax the update out of your phone now, you can go to Settings > General > About phone > Update center > System updates > Check now. LG suggests that you have your battery charged to at least 50% before starting the updating process. You might also want to consider a Wi-Fi connection so that your precious data allowance isn't used for the update. Also, you need to have 147MB of available space on your phone.
If you do own a T-Mobile branded LG G2, you can let us know whether or not you were able to install the latest Android build on your device by dropping us a comment in the box below.
source: T-Mobile via TmoNews