Strictly speaking, that is at odds with the literal and web definition of a lightbox, and as a result almost no lightbox lets you do what you are asking for. I say almost because there is one script (StripJS) that does this. This is supported by Photonic but not bundled with it because Strip is not GPL compatible. You can refer to the page where you select the lightbox for instructions about including Strip.
Realizing what I need is a slider not a lightbox, my bad.
I can link to a div-contained slider on a different page, but I have to be able to specify which image to show in the slider. Is there a way to link each image in a Photonic gallery to a unique url?
Photonic offers a slider layout (see example), but I doubt it will meet your requirement, which is too specialized and beyond the scope of Photonic or my support.