macOS 10.15 Catalina is now supported with the release of Serato DJ Lite 1.3
macOS 10.14 Mojave & 10.15 Catalina require the user to enable microphone access however, and without allowing access for Serato DJ Lite 1.3, you may experience severe audio issues.
You should be prompted by macOS when first launching Serato DJ Lite 1.3 (may require your Serato hardware to be connected), with the following messaging, in which you will need to choose 'OK' to allow:
Without doing so you will experience some of the issues listed above, but in case you chose 'Don't Allow' or ignored the prompt, you can also retrospectively adjust your settings to rectify permission (you will need to 'click the lock to make changes' and enter your log-in details to adjust the settings below):
NOTE: Even if you are using Serato DJ Lite, the setting below will still show as 'Serato DJ Pro' due to the way macOS recognises Serato software.
System Preferences → Security & Privacy → Privacy → Microphone → Serato DJ Pro → (enabled)
NOTE: Depending on your Serato hardware's need for internal inputs, you may not see the prompt for microphone access further above, or need to enable the microphone access under Security & Privacy.