Will a lip lift drop after a few months? (Photo)

There are surgical and non-surgical approaches to lip augmentation. Non-surgical approaches include botox (slight lift, reducing gum show) and filler (volume restoration). Surgically, you can have two separate incisions under the nose (italian), one incision under the nose (bull horn), one incision at the red/white upper lip junction (gull wing) or two separate incision at the corners, or a combination, depending on your desired look and anatomy. My preferred surgical technique is called the Elelyft, which is a version of the bullhorn approach.
There is definitely some degree of drop over time, but not back to the original unless very little was removed (

It's difficult to give you a meaningful feedback without seeing your full face & not knowing your face measurements such as philtrum. Generally speaking, some degree of drop with time may be experienced, but lips do not come back to the original state. This method produces long term results & typically does not need to be repeated, unlike fillers/ fat transfer.

best regards, 
Piotr Osuch, MD, PhD

Having performed many lip lifts I have never seen one return to its preoperative length. There is going to be about a 20% to 25% relapse by six months in studies that we have performed. The concern you should have with a lip lift in your case is what will happen if that is done alone. The lip lift affects only the central part of the upper lip, it does not lift the sides. With an upper lip lift in which the mouth corners are turned down and with some asymmetry, that will be magnified when the central upper lip is lifted. You may need to consider corner of mouth lifts or lateral vermilion advancements if you have a lip lift to avoid exacerbating these pre-existing lip issues..