Hi Jeff,
Interesting questions and yes doable, but there's a few things to think of, last I remember closing a popup that is open is going to give you a dumb warning something like 'host is trying to close window', and then you have to say 'yes' to it... Not 100% sure but that's usually the problem with doing a plain 'javascript:window.close();'
I suggest you try to work the LMP Thank you into the limitations of the popup window, the other option is offer a DHTML popup, sometimes called a 'hover popup', that basically sits on the page you are on, when submitted, you end up displaying in a full window (the current window) the Thank You page when it is submitted.
Good luck, let us know what you decide, got an URL to look at?