Been fiddling around a bit more with my Siri/HomeKit setup in order to get my Lyric Round Second Gen Thermostat to work and so far here is what I did:
I have a 4th gen Apple TV running TVOS 10.1 acting as Home Hub for remote access. I also have an iPhone 7 (iOS 10.2) and an iPad mini 4 (iOS 10.2). My HomeKit devices are Lyric thermostat and two iDevices switches.
I decided to setup my iPad mini 4 running as a Home hub (in addition to my Apple TV) to see if the problem was the Apple TV or something else... and here are my results:
(1) If I disconnect the lightning cable from the iPad mini 4 (remove it from power), Siri/HomeKit on my iPhone 7 for the Lyric begins to respond properly both when I am home (local wifi network) and away from home. Siri/HomeKit on my Apple TV will also respond correctly for the Lyric.
(2) Weird thing is when I connect the lightning cable to my iPad mini 4 acting as a home hub (plugged into power), when I am away from home the Lyric status in the Home App on my iPhone 7 will change to "No response". Also my Apple TV does not recognize the Lyric "sorry I didn't hear back from your devices."
(3) If I disable the iPad mini 4 as a home hub, when I am at home (same wifi network), my iPhone's Siri/HomeKit will recognize the Lyric (most of the time, there have been times when the Lyric displays a "no response" status). The Apple TV does not recognize the Lyric at all "sorry I didn't hear back from your devices." If I restart the Apple TV, it will recognize the Lyric for about a minute or so and then change back to "sorry I didn't hear back from your devices"
(4) When the iPad mini 4 is not a home hub and I am away from home, my iPhone's Siri/HomeKit will NOT recognize the Lyric "no response". Same with the Apple TV "sorry I didn't hear back from your devices."
I can reproduce these behaviors. And based on my experience I believe the issue is with the Apple TV not sustaining the connection to the Lyric thermostat in order to consistently provide a status update to my other iOS devices, particularly when I am away from home.
My two iDevices switches do not exhibit this behavior at all. Their Siri/HomeKit integration has been solid whether I am at home (same wifi network) or away from home and whether I only have the Apple TV as a home Hub or both the Apple TV and iPad mini 4 acting as a home hub (connected to power or not connected to power).
Apple PLEASE HELP!!