Because of the lack of alveolar bone support the lips will roll in making them look very thin. Aging will also contribute to vertical wrinkle lines. The best approach are vermilion advancements to roll the lips back. This is not only a permanent procedure but will also remove some of the vertical lines as well.
Lip filers should definitely help with the vertical lines and also help lift the lips to reduce the caved in appearance. Sometimes a bit of neurotoxin (Botox) can help also. Another option would be a thread lift. Choice of treatment will depend on clinical evaluation by an experienced doctor. Hope this helps.