Balms. Like body butter, balms don't contain water and they're usually applied to dry skin. You don't need to worry about a preservative.

Does homemade lip balm need preservative?

Yes, you need a preservative.

If it contains no water, and will not come into contact with water, or if you'll be using it immediately: No, you don't need a preservative.

What preservative is safe for lips?

Both Geogard 221 and Geogard ECT are recommended for use in lip products by the manufacturer. Anhydrous lip products (ones that don't contain any water) shouldn't need a broad spectrum preservative if kept dry.