How do I add cities to live weather on my Apple 13 phone?

if you need help with a 3rd party app, you should contact the app developer.

How to contact an app developer - Apple Support

When I search the App Store for Live Weather, I find Live Weather - Weather Radar by Fotoable, Inc. If this is the app you are referring to, they list contact info right in the app summary

(although it looks like the app hasn't been updated for 5 years, so unlikely there will be active support)