Can a Lich with Druid levels Shapeshift?

I was just pondering this the other day as a possible campaign villain. Although most Liches would be Sorcerers or Wizards, I don't see any requirements of becoming a Lich which state that a Druid can't become a Lich. At least in the SRD (which is the only source I have in front of me, I'm not sure if the Monster Manual or other books have more detailed information) the only requirements to be a Lich are:

Caster level 11 (which Druid counts towards)
Craft Wondrous Item

Now, the thing that makes this whole thing ODD... is that you have an Undead that will gain or loose a CON attribute. When it shapeshifts, it suddenly becomes "Alive". The Polymorph rules don't seem to strictly prohibit this as I read them.

Unfortunately, the Polymorph rules DO seem to prohibit a Lich from shapeshifting into UNDEAD animals, which I was originally going for. Undead is not listed as a valid type for Polymorph, just like you cannot shapeshift into a Construct.

I think for my villian I will do one of a couple of different things:

1) Make the Lich be able to shapeshift into living animals. It provides an excellent disguise for this undead druid abomination.

2) Make the Lich be able to shapeshift into living animals, and apply the Lich template to those animals. Since the Lich doesn't loose any applied templates when it Shapeshifts, you could argue that the Lich shapeshifts into a Bear, but that Bear has the same templates applied to it that the Lich does, which makes it into an undead creature, which retain all of the Lich's special attacks and special qualities.

3) Forget the Polymorph rules and make the Lich shapeshift into undead animals. Apply the "zombie" or "skeleton" templates to the animals that he shapeshifts into.

Personally I'm leaning towards number 2, but I don't know if that is supported by the rules or not.