Live only supports the following image file formats:
Alias(.als), Bitmap(.bmp), Cineon(.cin), Explore(.tdi), GIF, JPEG(.jpg), MAYA(.iff), PostScript(.esp), TIFF(.tif, .tiff), Targa(.tga), Wavefront(.rla). Unfortunately no, it doesn't support .avi movie files. You have to have a sequence of images.
You can convert your .avi movie into a tif sequence in something like Adobe Premiere, After Effects or Nothing Real Shake, if you have access to any of these programs.