Android 5.1.1 a k a latest version of lollipop is available for download for the Samsung Galaxy Note 10.1 2014 model. This ROM is made specifically for the P605 model but the developer says it would work just fine on the P607T.
It is said not to work on the P600 and P601. You should have Note 10.1 2014 TWRP on board in order to flash it. Here are the flashing instructions:
Reboot into recovery (volume up + power button for few seconds). Go into wipe menu. Select "Advanced Wipe". Check Dalvik Cache, System
Cache, Data and wipe them. Don’t reboot just yet.
Go into install.
Flash aosp-2015XXXX-lt03lte.zip
Flash GAPPS.zip
Flash SuperSU.zip
Reboot
Copy SuperSu and Gapps zip to /sdcard/OpenDelta/FlashAfterUpdate so that they are automatically applied after OTA update.
If internal storage is not being shown, connect your Note 10.1 2014 to the computer and type these commands into the ADB terminal.
su
restorecon -FR /data/media/0