Maybe too late, but here’s the solution.
Go into assets and choose the lightbox type you use. Check the Javascript file. Edit the part where he adds the http to the link. At the fancybox js it is at line 70.
@the Plugin-Author: Would be great if you could fix this for future updates (so my changes won’t get overwritten) – youtube always works with https, so there is no reason to keep the http line. It’s hard coded within 2 seconds. A flexible way such as he takes the exact URL that is stated in the front end would be perfect, but not necessary imho.