Can you get a lazy eye if something goes wrong during an eyebrow piercing?

Sure. It is possible since the nerve (one of two) goes right through there. Recommend off center piercing.
Lazy. Doubtful. If the needle used to pierce the eyebrow goes into your eye, or if you get an infection from the eyebrow piercing that spreads to your eye, then your vision could be affected. But this seems very unlikely. To get a lazy eye, this would have to occur in chldhood.
Not a true lazy eye. A true lazy eye is an eye that cannot see well because the part of the brain that receives information from that eye did not develop properly during childhood. Some people mistakenly call strabismus (crooked eyes, or eyes that look in different directions) a lazy eye. In the unlikely event that an eye-area piercing goes deep and causes an eye muscle infection or injury, strabismus could happen.