I have a few Tivo 4K's that I disabled the Streamer app and anything associate with it on the home page. I turned on the Channels button detector in the device settings. and wow everything works great on the tivo remote. Guide goes to channels guide Tivo button to library and live does go to the last channel watched on channels app but its slowwwww... getting there. Plus a few times when I press live again i takes you to the before last channel and back. That option at times throws you off the app and goes to the opening screen.
The Live button is not a real button, per se. TiVo modified the Android system to respond the the button, but it's being handled in some custom manner. Channels has to listen for the system responding to the button, then intercept it. The lag you are experiencing is because of the way TiVo implemented the button, and the fact that Channels can even react to it is a feat itself.