With an iPhone 7 and iOS 10, I can not reproduce the trouble you describe. Let me ask a few questions to see if it helps identify the problem quickly.
Are you running a release version of iOS 10, or are you possibly running a beta version of the OS?
Were you capturing DNG or JPG images, or both?
Other than capturing images, and then exiting the camera to see the folder "Lightroom Photos" did anything else significant happen? An app update, an iOS update?
Are you signed into your Adobe ID account during image capture, or not signed in? I checked and confirmed both cases do work fine on my own device. If you are not yet signed in, please do that -- this may at least get the images uploaded from the app cache to the cloud. Can you see the images when you sign into your account at lightroom.adobe.com or in the Lightroom desktop app?
Thanks for any additional details you can provide.
I'm am running a release version of iOS 10, not a beta. I'm on 10.0.1. Nothing else significant happened. I was taking photos on the plane, and at some point during the flight it stopped saving the photos and continues not to show them. I updated apps and restored the phone through iCloud on Friday when I got the phone so everything was up to date well before the problem began. I am always signed in on the app no matter what I'm doing with it. I'm writing this reply because I just now have access to my computer again, and I just checked lightroom.adobe.com and the photos are not there. Lightroom desktop looks like it's just seeing the photos from the first part of the plane ride, not any that aren't in lightroom.adobe.com or the iOS app.
OK, thanks for checking and getting back to me. I can't immediately explain the problem here, so I'll need to get some diagnostic info from your app. I'll send you a private message with instructions. If anything is learned that can benefit others, I'll be sure to post info publicly back on the thread here.
Thank you I'll check for your message and also post anything here that could help others.