Hi,
Thank you for the details!
I have checked the site, but currently the search is redirecting to the results page, the live results feature is not enabled. I assume you mean an infinite scroll feature for the results page, and not the plugin’s live results container?
That feature is not available for the results page unfortunately, it is usually a theme feature – if a theme has that. There are some plugins or custom coded solutions to create an infinite scroll for the results page, but because of how the theme has the control over the layout of that page, most will not work properly.
I usually advise not to use any infinite scrolling on the results page, as most solutions do not take the query arguments into account, and generate incorrect results.
Having it custom coded for the specific setup is probably the simplest way to deal with it, usually it is not too difficult, and will not generate much code overhead, and will work for sure.