What is the Safest Lip Filler?

The safest injectable for lip augmentation is one that can be dissolved if you don't like it.  The hyaluronic acid fillers like Juvederm and Restylane are probably the best and safest fillers on the market as risk is very low and they can be reversed with hyaluronidase.  Although they are not FDA approved for the lips, their use is very common and placement in the lips is considered  'off-label.' 

All FDA approved products are safe when administered by a licensed and experienced practitioner. Improve your outcome by choosing the right injector, not the product.

Juvederm or Restylane are hyaluronic acid fillers and last about 6 months at a cost of $550 per syringe which is usually 1 syringe for both lips. Collagen is cheaper at $450 per syringe but only lasts 1-2 months. Fat injections often look donald duck like and get lumpy so I don't advise them at all.
Good luck!