Numerous injectable fillers have been used for lip enlargement, usually with temporary results. Foam tubes, Goretex threads, other injectables, and even (not FDA-approved) liquid silicone injections have been tried and mostly rejected as "permanent" lip augmentation methods. The latter can harden, be lumpy, and even become infected and require removal (if possible).
For over 20 years I have been using dermal grafts (which may include tiny bits of attached fat but are mainly a 4-6mm strip of de-epithelialized dermis) from a patient's suprapubic area or from an existing surgical scar. The donor site is numbed with local anesthesia, and a 6mm wide strip of skin adjacent to an old scar (or making a new one if necessary) and about 7cm (close to 3 inches) long has the epidermis removed, and then the dermal graft is removed and rinsed in an antibiotic solution. The donor scar is closed with dissolving sutures. The lip(s) are also injected with local anesthesia, and tiny cuts are made in the corners of the mouth to allow passage of a 4mm blunt probe within the lip tissues. This probe gently separates, but does not cut, the lip tissues, after which the strip of tissue is attached to the probe tip, and the tissue graft seated in the lip tunnel as the probe is withdrawn. Two or three dissolving sutures in the lips and the living graft survives as a soft, permanent, natural lip enlargement. Swelling subsides in a week or so, and the results are beautifully subtle but definitely noticeable. The procedure can be repeated in several months if more enlargement is desired, but large grafts at one setting are not used as these are real living tissue grafts, and must be in contact with living tissue to survive and work.