I am planning on turning a recurring character in our current campaign into a Lich at an as-yet-undetermined point in the future. I know the DMG provides a template for doing this, but it would be nice to be able to use the Character Builder for this. I am using the last update of the Offline Character Builder.
No, the offline character builder never supported monster templates.
You may be asking the wrong question, the tool for Game Masters is "Adventure Tools."
From a theoretical perspective, it is impossible to apply "monster" templates to "player characters." The rules governing monsters and PCs are simply different. It is possible to give monsters powers that act similiar to what PCs have, and it's certainly possible to call them the same thing, but the fundamental mechanics are different.
Your best choice for a recurring villain is to use adventure tools to apply the lich template or to create a custom monster that matches your thematic requirements. While Adventure Tools does not support templates as templates, it's quite trivial to edit in a template's specific requirements.
There is a 3rd party app, cbloader, that can be used to extend and create new offline character builder content.
You may be able to use this to apply a lich template to your character.