T-Mobile's LG G3 users can manually update their phone to Android 5.0.1 right now
To manually update the T-Mobile LG G3, go to the sourcelink which will take you to LG’s mobile support tool website. Click on Software Update (LG Mobile Support Tool). You might see a notice saying that your software is up to date. That is usually a sign that you need to dry your eyes and try again another day. But not now! If you get the message that your phone is up to date, click on options and then upgrade recovery. This will install Android 5.0.1 on your LG G3.
Just to make sure you're covered in case something goes wrong, it would behoove you to back up your data and content before giving the mobile support tool a go. If taking this short cut makes you a little bit nervous, consider the alternative. You might have to sit through more waiting until T-Mobile finally decides it is time for you to install Android 5.0 on the LG G3. If impatience is your middle name, you could give the mobile support tool a shot. Imagine the looks of jealousy and admiration you will receive just by being the first T-Mobile LG G3 owner in the neighborhood to sport Android 5.0.1 on their handset.
source: LGMobileSupportTool via T-Mobile, AndroidAuthority