The sound part is a bit problematic yeah. The reason there's no sound during recording is because LFS doesn't get focus. So LFS remains quiet.
I have been thinking about fixing this back when I was working on it, but it's not exactly easy for me to do so for a couple reasons.
Because I didn't think many people turned out to use LFS Record, I couldn't really be bothered to investigate further. Maybe I'll need it for myself eventually, in which case i might look into it again.
And no, LFS Record isn't super easy to use. But the point of that is that you can get results that you can't get any other way. Maybe one should call LFS Record a specialist tool, rather than an overall video recording tool.