I've been running Outlook 2016 - Office 365 - 64 Bit - Click-to-Run since March, and never experienced this issue. I got the problem yesterday after updating Outlook 2016 to latest version. I am now running
Office 365 Version 1905 (Build 11629.20246 Click-to-Run ) - All apps are v16.0.11629.20238 64 bit
In my case, I tried to rename the .ost file and got a message that Excel was using my file, even though Excel wasn't running. I went to task manager, found Excel running in the background, killed it, and Outlook came immediately to life.
My questions are for Microsoft. If you're aware of this problem, what is the status? and is there a permanent work-around, or do we have to keep killing whichever Office App happens to be locking our .ost file. If you're not aware of it, please try to replicate it and feel free to contact me for any details you require.