EOS has beeswax in it. Baby Lips have no animal ingredients, but they are tested on animals. In fact, Maybelline, the company, tests everything on animals, so stay well away from them.
If you want a vegan lip balm try the "Hurraw! Balm" products: http://www.hurrawbalm.com/hurraw/
There are so many stores in NSW who stock it, so you won't have trouble finding it.
Hope I helped!
Soft lips have amazing lip balms, and from memory most flavours are vegan except for a few in the "naturals" range that contain beeswax.
Many 'Yes To' lip balms are vegan friendly also, but perhaps contact them directly for an updated list on which products are suitable.
Lush lip balms are also brilliant, though a bit more expensive.