I recently rooted two different Android Lollipop devices. On one device I was unable to flash (install) a custom recovery, and on the other device I was. This is a generic guide, make sure you have appropriate files for your specific device.

Note: I am in no way responsible for anything that happens your device if you happen to follow this guide.

Unlocked bootloader with custom recovery

Note: This requires a pc with compatible drivers installed and access to a custom recovery.

Find a custom recovery image. Easiest way to do this is searching for <Your device model> twrp.
Download the custom recovery image.
Download SuperSU flashable zip.
Copy over the downloaded zip to the internal SD card on your device.
Reboot to bootloader mode.
1. You can do this by using the hardware key combination. or
2. You can use adb (Android Debug Bridge)¹
  1. Enable Developer Options, by going to Settings → About Phone. Tap Build number a couple of times.
  2. Enable USB debugging, found in Settings → Developer options → Debugging.
  3. Plug in your device to your computer using usb cable
  4. If required, give your computer access to your device by accepting the popup
  5. Reboot to bootloader mode by using the following adb command: adb reboot bootloader
If not already connected, connect your device to your computer using usb cable
Hot-boot to custom recovery you downloaded earlier: fastboot boot
Flash the SuperSU zip downloaded earlier
Reboot device