I have smaller lateral incisors and need crown lengthening to correct it. How long does it take for lengthening to heal? (Photo)

Generally we like to wait between 6-8 weeks for crown lengthening to heal completely. If the area is in the smile zone, I would always wait a little longer 10-12 weeks for the bone and tissue to stabilize. 
Obviously these are just guidelines, and other factors need to be considered, including how much bone is removed and what type of gingival tissue you have.
Usually the gum tissue heals within a few days, so I wouldn't be so concerned with being swollen or having redness 2 months after the procedure. That being said, its probably best to hold off on the procedure until after your wedding. Surgery can be unpredictable, and even the most routine procedure can have complications, and the risk of that so close to your wedding is not advisable. You may want to see if you dentist can do a laser ginvectomy. Even though this wont give you a permanent results, it will help balance out the gingival heights, giving you a more attractive smile for your big day!
One thing to consider, after having crown lengthening done, you will have to put a veneer or crown on your tooth. Crown lengthening usually exposes the root of the tooth, which is always a darker shade than the enamel. A veneer will fix this and give you the best cosmetic result!

Hi:If you require bone removal then you should wait 3 months to be safe or at least 8 weeks after surgery.Best,Dr. Maddahi

If you did the crown lengthening now, by the time your wedding was here, you would probably be ok. It takes about 6-8 weeks of healing to look "normal" under most circumstances. It might be cutting it close.(no pun intended) I would avoid doing Botox. You have a great smile and ideally if that lateral was a bit longer your smile would be perfect, but that's ok. Your spouse will love you either way! The Botox will alter the way you smile and your smile might not feel natural for your wedding. I hope this helps!