You might see that the Dropbox Community team have been busy working on some major updates to the Community itself! So, here is some info on what’s changed, what’s staying the same and what you can expect from the Dropbox Community overall.
I want my lives to automatically save on DropBox and then when I come to DropBox and download it to my apple products I can still see them as Lives.
Yes, the Google Photos app does & has for quite a while. Here's an article from 2016 about it -> https://www.tomsguide.com/us/back-up-live-photos-google-photos,news-22359.html
It would be great to have this in Dropbox. I'm sure there are business and technical considerations, but it's been years & folks at Google, Apple & more recently Nextcloud have figured out ways to offer support -> https://nextcloud.com/blog/nextcloud-coherence-for-ios-a-completely-new-look-live-photo-support-new-image-pdf-viewer-quick-look-option-and-more/