You can have a locally running instance of FusionAuth. With this set up each page should be updated "live". For instance, if you make changes to an authorize page in a FreeMarker template, this should be typically visible on a refresh in the browser when you access the corresponding page.
However, there are improvements that can be made to the theme writing experience. You could consider also upvoting this feature request if this meets your requirements.
https://github.com/FusionAuth/fusionauth-issues/issues/582Otherwise, feel empowered to log a feature request that matches your use case below
https://github.com/FusionAuth/fusionauth-issues/issues/new/chooseThanks for the feedback!
Thanks,
Josh