AT&T G3 owners are getting the update they've been looking for today, as Android 5.0.1 finally has begun rolling out for the device. The new software version is D85020f, with an Android build number of LRX21Y (dated October 21, 2014).
The OTA should come down in the form of a 689MB package, which will take you approximately an eon to download from AT&T's decrepitly slow update server. Once you have it, the 5-minute or so install process will complete, and presto amazo: you've got Lollipop. What's new? Well, a lot - LG's revamped its notification shade and lock screen to be a bit more in line with Android's current layout on Nexus devices (though it's still not exactly what I'd call similar), and of course you'll notice the new software navigation button icons.
There's a full-ish list of Android 5.0 features here, but you'll have to remember that some of these features are limited to devices running more stock-like Android experiences. That said, you can add improved face unlock, trusted Bluetooth device unlock, screen pinning, the new device setup experience, and per-app notification controls (including priority notifications) to the list of stuff your G3 does. Notably, LG does not appear to have implemented Android's native multiuser mode on the G3 in this update, instead opting to keep its current "guest mode" system.
If you're having trouble downloading the update (like, it says there isn't one), just manually set your phone's date a couple days forward and try again - that should get it going.