Lazyload of images have become an important way to greatly improve page speed on Shopify Stores. We currently have it implemented on our site and it sped up the site considerably. Unfortunately all of the Judge.me widgets which show images do not get the LazyLoad benefit.
Our suggestion is to check to see if the site has lazy load implemented, and if so change the img tag to follow:
<img data-src="file.name" class="lazyload">
The JS is lazysizes.min.js that we used, but other implementations may use a different JS.