What procedure can turn my round eyes into more almond shaped eyes? Will a lateral brow lift help to elongate my eyes? (Photo)

Brow lift will NOT alter the eyelid. Almond eyes can be achieved by eyelid surgery but it differs depending on person's anatomy. See following link for details on almond eye surgery.

if you take your outter brows and lift them out and up, do you get the change that you desire? I would bet no. You do have a bit of a negative cant to your eyes (meaning the outter corner is slightly lower than the inner corner) and aesthetically pleasing eyes in a female should have a slight positive cant (opposite, outter corner 1-2mm higher than the inner corners). That can be corrected to a slight degree, but the shape of your eyes and facial bone structure really dictates the limits of what can be done and what cannot. 

The goal photo demonstrates someone with profound upper eyelid ptosis.  Her eyes look more cat like because of make up including false eyelashes and brow shaping.  I would start there.  The more radical approaches with rim implants and radical brow lifting often cause profound dysmorphic facial changes that push the face to the edge of the uncanny valley rather than being cosmetically helpful.