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.
Having the same problem.
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.