Lani,
High lip to ridge attachment occurs in many individuals.
This situation can certainly be a problem when constructing lower dentures.
The severity of the problem will dictate the surgery that will be necessary to resolve the situation.
In cases where the lip "cord" is the only hinderance then a frenectomy will usually solve the problem. The process requires the cord or muscle, connective tissue and fibrous tissue to be cut and/or lowered where it attaches to the bone.
If the cord is high and the adjacent tissue are high as well, (this can be visualized by looking in a mirror and pulling your lower lip from the center and seeing how deep the space between the lip and ridge are and then pulling your lower lip on each side and seeing how much space is available), then a frenectomy and vestibuloplasty may be required.
If there is insufficient bone then a bone graft may also be required to build up the boney ridge in conjunction with the above mentioned soft tissue surgeries.
On there own and together these are pretty standard pre-prosthetic sugeries done to accomodate lower dentures. In the situations I have seen they have been very successful and made many patients happy.
I perform this surgery in my office with local anaesthesia if no bone augmentation is required and the patient is healthy.
Like I said before, there is much that can be done to help stabilizing a lower denture.
All the best.
Mike