I wouldn't say it runs a "random ROM from the internet" - LineageOS is a very well-established project and is fully FOSS (free and open source software) except for firmware necessary for specific devices. It is the natural choice for any project, such as Waydroid, that requires good community support and ongoing availability.
Over a number of years, Google have progressively removed many of the original parts of AOSP (the FOSS foundation upon which Android is based), which means that alternative components have to be developed by projects like LineageOS. In spite of this, I suspect that LineageOS makes fewer modifications to AOSP than most phone vendors do, including Google themselves!
Over a number of years, Google have progressively removed many of the original parts of AOSP (the FOSS foundation upon which Android is based), which means that alternative components have to be developed by projects like LineageOS. In spite of this, I suspect that LineageOS makes fewer modifications to AOSP than most phone vendors do, including Google themselves!