Inserting a video lower third into Sony Vegas is quit simple. For a video lower third, you will want to make the background transparent. This can be accomplished using Chroma Key, but the results are not as good as the following method:
1. Open your existing video project in Vegas.
2. Right click on an existing video track (your top one is recommended) and select Insert Video Track.

3. You can drag and drop the lower third .mov directly into the new track you created if you have the folder open which contains the lower third graphic, or you can use the Explorer in Vegas to find the .mov, and then drag and drop it into your video timeline:

4. Right click the .mov file you just dropped, and select Properties.

5. In the Properties widnow that appears, choose the Media tab and scroll down to the Aplpha Channel section. Select Straight (unmatted) from the dropdown there and click OK.

That's it, your lower third should now have a transparent background.