Or would it be easier to somehow just go directly from the pastors channel to the TV. That way when the Mike is on muted it’ll play in the sanctuary and through the TV at the same time.
Lets separate the issues here:
1. Audio out of the board:
The X32 has 16 XLR outputs on the back of the console. To configure your output select the "routing" button to the right of the screen. Arrow over to the "analog out" tab. You can then patch an output, such as "output 4." This, of course, can be anything you want, it could be a direct out of the pastor's mic, or it could be a copy of your main feed.
I would recommend either a matrix or an aux for the output, this way you can mute and adjust the volume independent of the main mix/channel. You can also delay the send and EQ as is needed for the atrium speakers.
2. You need audio to get to the lobby.
There are many ways to do this, some of which have been suggested already. You may need to convert from XLR to something else (RCA, HDMI, ethernet etc). How this is done will depend on how you want to use audio in the Lobby.
3. Having audio in the lobby.
I would strongly advise against attempting to use TV speakers, they are not loud and they can sound horrifically bad. I am hesitant to make recommendations without understanding how large the space is, however here are a few suggestions.
A: A small powered PA speaker: Such as an a Yamaha DXR8. For most spaces, 1 or 2 of these would do the job. They would need to be fed an XLR signal and would require power.
B: Speaker Set with an amplifier. If it is a medium to small atrium perhaps get an inexpensive consumer stereo amplifier. This could effectively remain at FOH, and speaker wire (USE INSTALL GRADE!) would go to the speakers. For speakers you could check out
OTD Speakers I have had good luck with these in the past. I have bought several pairs for small projects over the years, all have sounded quite good for the money.
The AP840 has a decent amount of low end for the size. The AP520's are fairly detailed for the price, I was quite impressed for $60. The AP450's have zero low end, and are harsh sounding, however, they are also $30 and are much better than stock TV speakers
Hope that helps