I've had success with CamStudio Recorder and Microsoft Expression Encoder Screen Capture.
CamStudio looks like it'll record whatever's playing through the speakers, so if you have the "Listen to this device" box checked in Windows for your microphone you should be able to capture audio from your mic and some other media source at the same time. The Microsoft Expression Encoder will let you check off any number of playback or recording devices.
Neither program seems to generate video clips that can be directly used in Lightworks, though, so I've been using
avconv or
ffmpeg to transcode them, for example:
avconv -i ScreenCapture.wmv -f mp4 -vcodec libx264 -same_quant -acodec aac ConvertedClip.mp4