What is live source in your case? Some streaming protocol? I have no idea but for your second question: "capture avi" functionality is mostly the same in virtualdub/virtualdub2.
Virtualdub works with DirectShow sources: these are typically capture cards or web cameras, but software (called "source filter") can represent anything else.
Look here for example:
http://umediaserver.net/components/download.html
WebRTC DirectShow source filter
RTSP DirectShow source filter
RTMP DirectShow source filter
I never tried this. They say the filters provide uncompressed streams, so to view the picture you would also need decoder filters. Here things may get complicated.