How do I update a Craft website without losing data?
You can always add the fields manually to the live site, works best imo if you made a limited amount of changes.

If you have made a lot of changes, a plugin like Firstborn's Migration Manager could do the trick. I have never used it personally, but it seems to do a lot of great things and uses the built-in migration system of Craft 3. Probably worth to give it a spin. There's also a Craft 2 version.