I think probably the only way to do this is to have an Apple TV connected to the TV and “airplay” what is on the iPad screen to the TV.
(I’ve also got a Lumin–S1. Great stuff!)
Hmmm…not sure about the screen turning off. Perhaps there’s a setting that can prevent or delay this. I’ll have to mess around with one of mine to see.
Now that you mention it, I’m also curious. When I play Roon to one of my Apple TVs I’ve been just looking at the Apple TV default album/artist/track info, which itself goes to the Apple TV screen saver after a little while.
I agree it would be great to have the actual Roon screen on the TV for as long as you are listening.