Hello.
The Wix lightbox operates like a page. Therefore, if you attach a dropdown to a lightbox you can’t pin it to the site.
You can try using a container box or repeater instead. Checkout this Mega Menu example: https://www.wix.com/corvid/example/mega-menu
You can open a lightbox on a mouseIn event by calling lightbox open method here: https://www.wix.com/corvid/reference/wix-window.html#openLightbox
Good luck!