Today, Google has posted another factory image for the Nexus 6. This one is build LMY47E and it's still Android 5.1. Currently, it's unclear what is different in this factory image compared to the previous one which was LMY47D. The previous build was done on or around February 16th, with this newer build being done on the same day. So we're obviously looking at very small changes between these two updates. I currently have LMY47D on my Nexus 6, and am in the process of flashing LMY47E onto my Nexus 6 just to see whats new. It's possible that we could have the memory leak bug fixed with this update. That Google did say they had fixed internally, so it's possible. We'll have to hang on and see.
For those that need help flashing the factory image, first you'll need to go to this web page and grab the appropriate build for your device. Now you'll need to make sure you have the Android SDK set up and installed. Next unzip the factory image into the SDK/platform-tools folder on your computer. It's important to make sure they are unzipped into their own folder inside that one. Now you'll need to open a command prompt window from inside the platform-tools folder. You'll now be typing in the following commands (obviously you'll swap out the "<filename>" for the actual filenames in that factory image.
adb reboot bootloader
fastboot flash bootloader <filename>.img
fastboot flash radio<filename>.img
fastboot -w update<filename>.zip
Now if you want to unlock the bootloader, simply type "Fastboot oem unlock" from the command prompt. Should be unlocked in a few seconds, next press the power button on your Nexus 6 and you should be all set. It may take a bit longer to boot up, as it is completely fresh and needs to build the cache and update apps that are already installed on the device.
If you are running the LMY47D, I wouldn't make a big deal about updating to LMY47E, as it's likely a very small change, seeing as it was built the same day as the previous build that's rolling out to everyone else.