Unfortunately no, it's not possible to open a non-JIG thumbnail or text link to open in a lightbox of JIG. Assuming you mean prettyPhoto and/or PhotoSwipe. The technical explanation is provided so you can better understand why.
The lightboxes in Justified Image Grid are not meant to replace your theme's solution, nor they should extend beyond JIG. This is to avoid conflicts such as opening double lightboxes and to allow a closer symbiosis with JIG's proprietary layouts. Certain lightboxes, especially the main ones (prettyPhoto and PhotoSwipe) have been customized for better social sharing with smart deeplinking. These require the thumbnails to be set up in a particular way (including the content ID and image size information) and server side support from JIG itself. The benefits of these customizations would not be available outside JIG, in other words the lightboxes would not work the way you want them to.
If you wish to use a 3rd party lightbox then by all means yes, you can have it open from JIG thumbnails and as also from single images in your content. These include:
- Social Gallery
- Jetpack Carousel
- Your theme's built-in lightbox could be used as a custom lightbox in JIG, provided you set up the custom class, rel and/or data-attributes for the thumbnail link. Thes are available at the Lightboxes tab > Link attributes (also for custom lightbox) section.
- Most other separately installed lightbox plugins. These may include Magnific Popup or ColorBox.