The Codesigning performed by Xcode is not sufficient to get this app working on Mojave (macOS 10.14). You have to force the replacement of the signature within the embedded scripting additions
codesign -s "Developer ID Application: Mark Alldritt (Z7S6X96M3X)" --force --deep ~/Desktop/LNSOSAX.app/
UPDATE
For the LNSOSAX, this does not work because the embedded scripting additions where never codesigned. For the app to work on Mojave, each of the embedded scription additions must be codesigned using the above command. Then, the entire app needs to be codesigned.