I have tried mirroring the iPad display but the projected result is a low-resolution, apparently 3:4 aspect ratio image. Although streaming of web-based content continue to work fine after this, mirroring continues to be locked in the faulty format (even with another iPad) and the only way I have found to rectify the problem is to restart the entire system (wireless router, ATV, AV amplifier and projector). Restarting just the ATV is useless.
Lightroom mobile does not have native airplay support for Apple TV. However, I have found that airplay mirroring works very well for displaying photos from lightroom mobile. It appears on my TV filling the screen with each photo at excellent resolution (not the low resolution 3:4 aspect reported by another user.) There are many caveats to make this happen. Here is my setup:
As of February 24, 2014
Apple TV generation 3
Apple TV firmware updated to latest available (2 hours ago)
Iphone 6 with IOS 8.1.3, lightroom mobile 1.3.1
Ipad air (A7 processor, retina display) with IOS 8.1.3, lightroom mobile 1.3.1
USE LIGHTROOM MOBILE IN PRESENT MODE (IMPORTANT!)
Your question prompted me to even consider this possibility. It works so well, I will use it all the time with the family at home.
Mirror mode shows just the iPad's window which is 4:3 so on an HDTV there are black bars on the right and left side of the displayed/mirrored iPad screen. Even in LR present mode you'd still be just mirroring a 4:3 device on a 16:9 device unless LR Mobile now has native Airplay support allowing full 16x9 screen broadcasting of your photos.
What I'm trying to avoid are those clumsy black bars on the sides that the Mirror workaround doesn't address. It sounds like you're saying LR mobile has native Airplay support or you're just ignoring the black bars on the sides of your TV.
I'd use the iPad's native photo app to share pics if it would allow you to sort by filename instead of automatically sorting albums by capture time...