If you want to experience latest Android 5.1 with root for your Galaxy Note 2, you may want to try the latest CyanideL ROM, available for AT&T, T-Mobile, Verizon, and GT-N7105 Note 2 as Android 5.1 and Sprint Note 2 as Android 5.0.2 Lollipop.
This is definitely one solid ROM that’s stable and comes loaded with more features than you can ask for. Also, you can use Shift kernel along with this ROM, which gives you awesome performance boost with 1.8Ghz overclocking (that’s what I recommend although you can go higher) along with STweaks app.
With STweaks app, you will be able to further customize your CPU, GPU, sound, display, and much more. This alone is awesome way to tweak the performance and features on your phone.
Wait, that’s not all, the CyanideL ROM allows you to fully customize your phone including your status bar, navigation bar, notifications, power menu (add native screen recording), system animations, and much more. My favorite feature is the ability to disable your hardware buttons and enable soft buttons, which you can also customize with more than 3 default buttons with shortcuts to your favorite apps. This is a feature that only existed with OnePlus One CM11S and CM12S stock ROMs but now you can get it on your Note 2.