We had some continuing issues with Salesforce Inbox for Outlook and then Lightning for Outlook with Einstein Capture / Inbox. For us after all of the trusted sites had been removed ( also the Microsoft related ones to Azure AD, O365 e.t.c ) from the group policy in our network for IE ( since IE is the rending engine for Outlook web addins ) then we could get this work as expected.

Now there are no Microsoft / Salesforce related trusted sites for us at all and actually we just have our internal network in local intranet zone and it's working great for us. The issue is around cookies and information traversing the protected mode and non-protected mode of IE and is quite annoying and hard to debug.