If Local isn’t relaunching and updating after the download completes, please open Terminal and run the following commands. Some may require your password. If so, simply enter it and press Enter.
Note: Some of these commands may fail due to files/folders not existing. If you do see an error about a file/folder not existing, ignore it and move to the next command.
xattr -dr com.apple.quarantine /Applications/Local\ by\ Flywheel.app
sudo chown -R $(whoami) ~/Library/Caches
sudo chown -R $(whoami) ~/Library/Application\ Support/com.getflywheel.local.ShipIt
sudo chown -R $(whoami) /Applications/Local\ by\ Flywheel.app