The solution is to not use the form embed code, for indeed it's geared toward third-party pages.
Use the integrated LP form component, but hide the form. Then move the form into the lightbox when the lightbox shows.
A front-end developer will be able to do this for you.
Solved what I needed by using a filter of Fills Out Form with a Referrer that contains part of the link.
Yes, you can build Smart Lists to extract the activities, but that still doesn't link the form as an LP Conversion.