Based on the photos, the asymmetry at the right corner of the mouth appears to be more related to soft-tissue movement and the way the corner of the mouth sits during smiling rather than something that would typically be corrected with a traditional lip lift. A lip lift primarily changes the distance between the upper lip and the nose and can increase the amount of upper lip show. It generally would not be my first choice for an isolated gap at one corner of the mouth. Filler may be helpful, particularly if there is a small volume deficiency or depression around the corner of the mouth. A very conservative amount can sometimes soften the indentation and improve symmetry. However, the goal should be subtle correction rather than simply filling the entire area, because too much filler around the mouth can make the lips look heavy or alter the way they move when you smile. Another consideration is the underlying muscle movement. If the asymmetry becomes significantly more noticeable when you smile, neuromodulator treatment in carefully selected muscles can occasionally help balance the movement, but this needs to be done very conservatively because weakening the wrong muscle can temporarily affect your smile. Since you mention that this has become more noticeable with age, some combination of volume loss, changes in skin elasticity, and normal facial asymmetry may be contributing. A small, targeted correction is generally preferable to a larger procedure when the issue is localized to one corner. The most important point is to determine whether the gap is present at rest, only with smiling, or both. That distinction helps determine whether filler, a neuromodulator, or simply leaving the area alone would give the most natural result.