Well one possible reason is the DVD audio is out of sync but you never notice it as the track is told to play with a delay is miliseconds to offset that. Not all DVD rip tools take this into account.
Try this and see if the same thing happens
1) Rip the DVD to hard drive using
MakeMKV, this does not convert the video it simply copies the MPEG-2 video from the DVD to a standalone .mkv container so you have a MPEG-2/MKV video. MakeMKV is quite good at detecting the delays on DVD audio tracks and embeds that information into the mkv container so an encoder sees the preset delay.
2) You will need a more modern XviD encoder than AutoGK in order to open MPEG-2/MKV videos, try
XviD4PSP - download the beta version in that link.
Set format = AVI, set codec = XviD, set audio = MP3 (most of this is preset when selecting AVI).
If the video turns out okay then that was probably the cause, if it doesn't try one more XviD encoder just in case like
Staxrip which was designed for use with MakeMKV, though it's rather annoying to setup/install.
All of the above are free software. Failing all of the above you could try something like
Freemake which is one of those basic encoders, maybe it will get lucky.