Audio/video synchronization problems are normally caused in the conversion process from avi to dvd-video format. This is sometimes caused by having mp3 audio in the avi that is encoded using variable bitrate. Lesser quality encoders sometimes have problems with this particular type of audio. Don't know for certain that this is what is happening to you, but it is a common occurrence.
You should try a different encoder and see if this helps the situation. FAVC, AVStoDVD and DVDFlick are all free to use and will give you a finished dvd ready to burn to a disk. Of those, I'd probably try AVStoDVD first. FAVC and AVStoDVD can both use the HCenc encoder, which is far superior to most mpeg2 encoders you'll find in all-in-one avi to dvd programs.
If you want to try to salvage the out of sync dvd video you have now, you can try the free trial of VideoReDo TV Suite. It has a tool called the QuickStream Fix tool, which can often times solve this problem. There is also another audio/video sync tool within the program, but is not as simple to use.