Pre-select dropdown lightbox-based form field

I have searched and read the similar-sounding articles to do this, but I’m a little lost where to start.

First things first, this is the page I want to amend:

What I’d like to do is automatically select the field campaign_choice with the relevant campaign information based on which “Build my campaign” button is used.

The problem I’m having is that because the button just shows a form in a light box, I don’t see where I could add code or variables.

Any pointers please?

Thanks in advance