A Lateral Brow Lift is performed through a small incision in the temple area and the scalp is dissection and pulled upward raising the latweral brow. The healing time typically is several days. That's the good news, now for the bad news.
Lateral brow Lifts are usually reserved, IMHO, for women who have the proper arch and position of the medial and central portions of the eyebrows but the outside (lateral) portion has fallen. This is important because a Lateral Brow Lift does not dissect the eyebrow tissues completely off of the superior orbital bone like a formal Brow Lift procedure and as a such has limited ability (an longevity) to lift the brows.
From your photo, it appears that the entire left eyebrow is low inposition and flat without arching in the medial and central regions which means the lateral Brow Lift will have a marginal effect at raising the eyebrow.
IMHO, you should consider a Coronal Brow Lift that is capable of raising bot eyebrows along their entire length. The incision can be hidden 3 inches within the hairline and if performed properl, IMO, will not raise the frontal hairline along the center section.