Verizon really isn't on the ball with its Note 4 updates. When Google released the Android 5.1 source code in March of 2015, the Note 4 was only half a year old and it was still one of the most expensive flagships being sold by the operator. Now sure, Samsung took its sweet time to have Android 5.1 ready for everyone, but by the beginning of August, Sprint had already released it. AT&T followed in October, and T-Mobile at the end of November.
Verizon? Well, as the largest carrier in the US, customers would have assumed that their operator would be burning the midnight oil trying to get the update out to them as soon as possible. But that wasn't true and it left users furious, as evidenced by this thread on Verizon's community forums. Over 720 replies were posted from users lamenting the inexplicably long delay in getting Android 5.1.1 on the Note 4, which was made even more intolerable because of the many bugs and stability issues that they were facing on Android 5.0.
But that wait is about to wind down, finally. Verizon updated its support page for the Note 4, citing software version LMY47X.N910VVRU2BOK3 based on Android 5.1.1 with Android for Work, security and bug fixes, and Samsung Knox upgrades. The new version also takes out the Amazon Appstore and Widgets from the Note 4.
The OTA should be rolling out soon to everyone on Verizon, so start your update engines and hope for the best. Specifically, hope that those pesky bugs are really gone and that your device is functioning smoothly now.