Refresh current page (without reloading elements) on lightbox close

Have you just tried passing the data from the lightbox to the page?
https://www.wix.com/corvid/reference/wix-window.lightbox.html

How do I pass data between a page and a lightbox?
When you open a lightbox using the openLightbox() function, you can pass an object containing data to be used in the lightbox. In the lightbox’s code, you call the getContext() function to retrieve the data sent by the openLightbox() function.

When you close the lightbox using the close() function, you can pass an object containing data to be used by the page that opened the lightbox. This data is retrieved from the resolution of the Promise returned by the openLightbox() function.

If you read the API reference you will find code examples that you can look at.