What matters is… what does it actually render as, check the source of the actual website in the browser: ctrl+u
As for lazyloading as a feature that’s only the part that loads the script, it does not account for what the rest of the theme may or may not be doing.
Past that realize your asking a massively broad question that is beyond a simple forum contribution about a custom implementation for a common web-development pattern.
If you need this website speed theme customization done for you and have the budget then contact me by my email for services. Contact info in forum signature.
ALWAYS please provide context, examples: store url, theme name, post url(s) , or any further detail in ALL correspondence.
This is Richard from PageFly - Shopify Page Builder App
Using an external library for what already exists for your theme is not an optimal way.
Instead of adding the library which changes no thing or even slow down your site, i suggest you should check on your theme script and enable it. Infact its just an image attribute as loading=“lazy”