I had explained what Mark has just stated but it was gobbled up in cyberspace

AVI is not a "format"
To reiterate. DV AVi from say a MiniDV camcorder will join up without any need to reeencode any part that dont need it.
It is however possible that your "avi"s are derived from mpeg4.,divx, xvid or even mjpeg files
These compressed files are generally going to lose PQ as they are meant to be viewed, not editable files as such
As such , they may derive from differnt codecs, and in joining them you would be reeencoding and this is never "lossless".
If they are all divx files, it might be possible to use products like Dr Divx or DIVX pro to Edit" them with minimum quality loss