Finding all photos with the same 2 people in it.

If you use the Lightroom Desktop app on your PC, you should be able to do that provided you have used either the People tagging or keyword functions to identify the people in each photo. Once that's done it's a fairly simple process to use the search function to first isolate all photos containing Person A, then searching all those resulting photos to find which of them also contain Person B. 

I don't think that's possible in the LrMobile app, but can be done using the LrDesktop app.

You can use the People Feature to tag people's faces, here's Adobe's documentation:

https://helpx.adobe.com/lightroom-cc/using/people-view.html

You should then be able to use the Filter icon to select the names you want to search for.