It looks like there is some mixed content called out in your console.
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.
As a first step you can try running a search and replace command to help clean up any mixed content type errors. To do this you can simply click on Open Site Shell in your Local app under your site name. The command would look something like this:
You’ll also want to make sure you Trust Local’s SSL certificate, to help avoid insecure content as well.
If you’re still noticing issues, check to see if you have plugins or themes that retain caching or have a “Regenerate CSS” option. These may need to be refreshed in order for changes to be displayed.
There may be other plugins getting in the way as well if they are trying to force SSL/HTTPS.
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.
As another workaround, if you’re still having trouble, you could try pushing the site up to a Demo to see how it looks there. Flywheel offers free 14 day Demos that you could test out: Demo Site