Live Links don’t match your Local Site URL (ie: mysite.local), so Local attempts to rewrite these on the fly. Live Links is broadly compatible with many themes, plugins, and custom code snippets. However, some images, front-end assets, or other HTML elements may be missing from your site when viewing it over Live Links. Try the tips below:
Run the following WP-CLI command wp search-replace 'SITEURL' 'LOCALURL' --skip-columns=guid
Disable certain types of plugins: caching, security, force HTTPS/SSL
If you’re still having issues you might open up the console of the page and see what errors are present. Is it still showing some mixed content or some other type of issue?
You might try viewing it in an incognito window, a different browser, or over LTE Data instead of WiFi to see if caching is getting in the way as well.
Elementor also has a Regenerate CSS option that you may need to utilize as well to refresh things:
If you click Open Site Shell in your Local app under your site name it will open a shell window in which you can run WP CLI commands. You can also clean up mixed content with plugins as well like Redirection