Looks like I was not alone (a comment from 2012):
"A further improvement would be if one could also submit the url of the
current page to launchy as well. But I am already very satisfied with it as
it is :)"
Source:
https://addons.mozilla.org/en-US/firefox/addon/launchy/reviews/?page=2
Too bad :(
Reading the sources, I see some Js.
I just found that window.location.href can get the webpage's URL.
I think I'll just try to contact the author. I'd need to understand the whole
thing before attempting anything, and that's beyond my super powers for now.
But with that feature, Launchy would be perfect. And youtube-dl would be
unstoppable.