Earlier today, the folks at Google have uploaded Android 5.0.1 Release 1 Lollipop update to AOSP. Now, the Nexus 10 Android 5.0.1 Lollipop LRX22C factory image is available for download. For what it's worth, Google has released the 5.0.1 factory images for Nexus 7 2013 WiFi and Nexus 9, as well.
The new Nexus 10 Android 5.0.1 Lollipop update only arrives with minor changes, so don't get your expectations too high. For the time being, there's no official changelog available, but the new release is most likely aimed to fix some bugs and improve the overall performance of Lollipop. It's also worth mentioning that the new build is labelled LRX22C.
The release of the Nexus 10 Android 5.0.1 Lollipop factory image also suggests that the OTA update should follow soon, even though there are currently no users reporting that the new firmware is hitting their devices. As you may know already, you will be able to use the Android 5.0.1 factory image to update your Nexus 10. After you download the Nexus 10 Android 5.0.1 Lollipop factory image from here, all you need to do is adb side load it to your device. Note that all all the data on your device will be lost in the process. Even though for certain devices you can avoid performing a full wipe by removing '-w' from the flash-all.bat script, it seems that this work around doesn't work for the Nexus 10. Or at least that's what the users are reporting.
Even though flashing the Android 5.0.1 Lollipop factory image is, at the moment, the only way to get the new firmware on your device, we are advising you to wait until the OTA update is released. The Android 5.0.1 update is not that major to be worth having to perform a factory reset. Anyway, if you still want to install the 5.0.1 LRX22C factory image on your Nexus 10 and you have no idea how to do it, return to this post later today when it will get updated with a link to a tutorial that teaches you how to flash Android 5.0.1 factory image on Nexus 10.