Ok, so I'm trying to post to a once-a-week schedule, and one of the things I want to do more of is to share the useful resources I've found around the internet.
One of those resources is Knotions E-Magazine.
In addition to publishing a bunch of free patterns, (many of which have definitely caught my eye) they also produce tutorials, and it was their tutorials that I found when I was frantically searching the internet wondering what an LKI stitch was.
Answer: An LKI stitch is a Left Knitted Increase (or, as Knotions puts it, a Left Lifted Increase).
This was the first tutorial that made sense to me on how to do the lifted increases. Though I personally still prefer the M1 (M1L is my direct preference unless there's a reason for M1R), the Lifted Increases can be easily done, aren't fiddly, and aren't difficult to do with purl stitches, so I definitely see the appeal.
The only downside from a designer's perspective, is I find that the lifted increases have more of a slant to them then the various M1 increases. So I have to consider the direction that the stitches are/will be traveling. That could be my own knitting style, though. I've also noticed that the lifted increases don't seem as common as some of the other increases, but the knitting lexicon of stitches is always changing, so lifted increases may become more common.
Anyway, I've linked the Lifted Increase tutorial further up in this post, and I'm also adding a Resource Link for the many technique tutorials published by Knotions, in the hopes that people will find them useful!