Rhinoplasty and Lip Length
The specific maneuvers of a rhinoplasty will not make the lip drop down lower. But lifting of the tip and correction of a hanging columella can make it appear to look longer as the nose moves upward.
Lip and nose
The distance between the lip and nose should not change. However, with the tip lifted it may appear a bit longer
Increase in the distance between the upper lip and the nose from a rhinoplasty
When performing a rhinoplasty for the droopy tip, the tip is lifted which gives the appearance of a longer upper lip. It is also important to release the depressor septi ligament which pulls the tip down when smiling. Reduction of the hanging columella is accomplished with a columella-plasty. This involves removal of excess skin and cartilage and lifting the columella upwards, which also gives the illusion of the longer upper lip. For many examples, please see the link and the video below