Media Library images might be shown in preview, but not be available on a live site, when changing the LinkProvider and mediaUrlBuilder/urlBuilder to lowerCaseUrls=true. The issue arises if media items are not republished to update the URLs on Sitecore Experience Edge. At this point, media links are generated with lowercase URLs, which are different from the media URLs on Experience Edge.
The root cause of the issue is that media URLs in Sitecore Experience Edge are case-sensitive.
To ensure that the media URLs work when lowercase URLs are used:
<lowercaseUrls>true</lowercaseUrls>