Today I saw an update of the Outlook for iOS app (4.2313.0) and after installing I could finally turn on and configure the Authenticator Lite.
I still have one finding. When I test the MFA prompt my "normal" MS Authenticator gets a push notification but the Authenticator Lite does not, even though push notifications are enabled.
It look like if you have 2 phones, 1 with the lite and 1 with the normal authentiactor you don't get push notifications on the phone with the lite version. Is this by design?
What I can do on the MFA screen is choose another MFA and then choose the Authenticator Lite, that is working. But not through a push-notification.