The 3rd-gen Fire TV Stick and the Fire TV Stick Lite have been rooted. XDA forum user k4y0z has posted instructions for how to root either device, which currently requires the Firestick be on Fire OS version 22.214.171.124 or older. They’ve also provided a build of TWRP custom recovery to allow for the installation of custom ROMs. XDA forum user Rortiz2 has already created a custom ROM for the latest Fire TV Sticks based on LineageOS and Android 11.
For those unfamiliar with the world of rooting and ROMs, here’s a bit of info to set the stage. Unlike simpler modifications, like sideloading and changing settings through ADB commands, rooting a Fire TV provides full unrestricted access to change any aspect of the device’s software, including the installation of an entirely different operating system, referred to as a custom ROM. If a device is rooted, you don’t have to install a custom ROM, but that is usually the next step. The utility on Android devices, like Fire TVs, that facilitates the installation of the operating system is simply called recovery. Once a device is rooted, a custom recovery is installed to be used to install custom ROMs. TWRP is the variant of custom recovery that has been made compatible with Fire TV Sticks in this case and LineageOS is the variant of Android 11 that has been used to make a custom ROM for installation on Fire TV Sticks.
With the installation of LeneageOS on a Fire TV Stick, the device essentially becomes an Android/Google TV device with Google’s home screen, instead of Amazon’s, and access to the Google Play Store, instead of the Amazon Appstore. That may sound like an intriguing proposition, but be aware that making such a drastic change to the device often comes with bugs and issues, especially if done at this point when the software being created is so new. Not to mention the large risk of bricking the device, making it unusable, if you make mistakes. You should, at least, read through both the rooting thread and the custom ROM thread on XDA in their entirety before attempting this modification on your Fire TV Stick to know what issues have already been uncovered.