Mac OS X 10.4 - Thunderbird 3 to Thunderbird 13
It seems that installing Thunderbird 3 on a newer Mac--non PowerPC--is the correct way to go about it.

I'll refer to the older Mac as "machine 1," and the newer Mac as "machine 2."


Find an archived installer for Thunderbird 3.
Install Thunderbird 3 on machine 2, and launch it.  Do not answer any questions, and quit Thunderbird: this will generate the appropriate folder structure in ~/Library.
On machine 1 locate the applicable profile in ~/Library/Thunderbird/Profiles/, and copy it over to machine 2.

I archived it with tar -cf ~/Desktop ~/Library/Thunderbird/Profiles/profile so it transferred faster, and saved a copy to our fileserver.

On machine 2, place the profile in ~/Library/Thunderbird/Profiles, keeping in mind that in Mac OS X Lion ~/Library is hidden in Finder.

Extract the profile with tar -xzf ~/Library/Thunderbird/Profiles/profile.tar.gz.

Copy the name of the generated profile to the clipboard, and delete it.  Then rename the profile you copied from machine 1 to the name of the generated profile.
Launch Thunderbird, and you should be good to go!