How do I set up Luna on Catalina?
Along with enabling Accessibility, which was introduced with macOS Mojave, a new permissions has been added with macOS Catalina. "Allow Screen Recording" must be enabled to allow Luna Display to access the content on your screen. Luna Display does not record the contents of your screen, but since it is acting as an additional display, this permission is now needed.
There will be a message that prompts during initial setup, with detailed steps to Enable this from your Mac's Systems Preferences.
You can also activate this manually by going to System Preferences, Security & Privacy, under the Privacy tab. There, scroll for "Screen Recording" and check the box next to the Luna Display icon.