The lens profile function is the main reason why I use Lightroom Classic CC on Windows 10 instead of sticking to the iOS app. Having the ability to use lens profiles in the mobile app would make things a lot easier.
What do you mean when you say 'default lens profile'? Most of the lenses I use are vintage and don't transfer any EXIF data, so I just select from the roll-down list whenever I'm in Classic.
Ah yes, that won't work for you then. The default profile would be the one automatically selected in the pop-ups, but without metadata, it won't be able to do that.