Fortunately, it looks like your wait will soon be over, as T-Mobile's senior product manager, Des Smith, recently took to Twitter to announce that the update was approved by the testing team and will start rolling out soon.
In Europe, the LG G3 was updated to Android 5.0 Lollipop as early as December, and even Verizon was able to beat T-Mobile to the punch by rolling out the update a couple of months ago. T-Mobile started testing the new software version for the LG G3 back in early April as well, but it looks like something went wrong with the update, and a new build had to be created.
LG's implementation of Android 5.0 Lollipop on the LG G3 brings all the things that make Lollipop a significant step forward compared to Android 4.4 KitKat, such as a new user interface, a new lock screen, a new multitasking screen, as well as the new 64-bit ART runtime.
At the moment, we don't have any further details, such as an exact release date for the OTA update or more info on the extra goodies (if any) that the update will bring, but we'll let you know as soon as more information is available.
source: Des Smith