In lightbox.css make the highlighted additions/changes:
That won't be perfect. The overlay will cover the whole screen though. The only problem remaining is that if the window isn't tall enough and you scroll the window to see the bottom of the lightbox, you still get those horizontal lines at the bottom. But at least they're behind the overlay now. And, when you dismiss the lightbox, they go away. BTW, if you resize the window to see the bottom of the lightbox, there's no problem. And this won't work in IE 6. But I don't think we need to worry about that browser. Do you? I mean almost no one uses it these days.
width: 100% !important;
height: 100% !important;
Oh, and I don't think you need jQuery any more. If not, get rid of that script.