@mrbrownstone-1
Have looked at your theme – but without downloading it (it is a Premium theme) – we cannot tell for sure, but am almost certain that the reason a3 Lazy Load is not applied to the sites home page is because the theme developer adds images by a custom function. It is impossible for a3 Lazy Load to know what custom function a developer creates to do that.
a3 Lazy Load has a number of filters that any theme developer can use to add to their custom functions so that a3 lazy load can find them and be applied.
This is the support ticket that I posted for @friendofmisery as his theme is a free one from the WordPress Repo. I would have posted a ticket for you as well on your theme developer – but obviously can’t do that as it is a Premium theme.
If you would like to create a ticket with your theme developer – requesting that they add the filter to their custom function for a3 Lazy Load support you can copy a lot of the ticket that I posted.
Regards
Steve