Update: I was able to make Au Lab show permission request, finally. I think the reason it didn't ask permission before was that it was somehow cached since I had Au Lab in my /Applications before updating to Mojave.
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It did request permission when I downloaded new version from iTunes - Mastered for iTunes - Apple (CA), unzipped it right in my Downloads folder and launched it from there, without moving to /Applications folder. That's when it said it's an app downloaded from the internet are you sure bla bla and then when I created document it asked for permission.
After that you can delete Au Lab copy from Downloads and continue launching from /Applications — it'll work.
Oct 3, 2018 2:16 PM