A quick question for those who have had LIS. My understanding is that the incision for this procedure is outside of the anal canal, but many of the posts I've read seem to indicate otherwise. Anyone willing to share a little bit of detail about the procedure?

Here is an excellent article on anal fissures generally, their diagnosis and evaluation, treatments and outcomes.
http://www.medicinenet.com/anal_fissure/article.htm
Here is a paragraph from that site on the LIS surgery:
Surgical treatment. The Standard Task Force of the American Society of Colon and Rectal Surgeons has recommended a surgical procedure called partial lateral internal sphincterotomy as the technique of choice for the treatment of anal fissures. In this procedure, the internal anal sphincter is cut starting at its distal most end at the anal verge and extending into the anal canal for a distance equal to that of the fissure. The cut may extend to the dentate line, but not farther. The sphincter can be divided in a closed (percutaneous ) fashion by tunneling under the anoderm or in an open fashion by cutting through the anoderm. The cut is made on the left or right side of the anus, hence the name "partial lateral internal sphincterotomy." The posterior midline, where the fissure usually is located, is avoided for fear of accentuating the posterior weakness of the muscle surrounding the anal canal.

The incision the doc made to access the internal anal sphincter is on the outside. I had the surgery and the incision is still bothering me so I'm hyper aware of where it is!
Also, I watched a video clip of the procedure that I found while googling lis. You may find that helpful...gross...but helpful.

My LIS incision is to the left of the anus and internal, not visible from the outside, but I can still feel slight pain from the incision site and fissure site 5 weeks post-op, like you next, I'm hyper aware too!