The usual approach to handle similar problem is more or less the same.  You have to check what  Android app-activity/service is being initiated when captive portal login pop up while there is no lockdown mode enabled on your device of interest.  Then add the found bundle-ID and/or activity name in the lockdown/application-run-control whitelist to allow  normal pop-up when lockdown mode is re-enabled.

This is an interesting data point - I believe that the item being run is com.android.captiveportallogin - or that is what appears to be being called when you tap the notification if you pull down the notifications list from the status bar.  I think it must be enabled or whitelisted already because when I run the lockdown with the status bar enabled then I can pull down, click on the notification and it runs fine.  But when the status bar is disabled the user has no way to access the notification so no way to trigger the captive portal login.

I basically just want the device to detect the presence of the captive portal (it does this already because it creates a notification even though I can't access it) and open the control to complete the login.