((((((( The first stitch on any row is K1 as I recall - why couldn't it be added to with more stitches in a K3, 4 or 5, P3, 4 or 5, Moss st, seed st, etc., just by adding the right number of stitches. You'd do your first YO drop, K1 later in the lace row to how many extra stitches were added. K on an extra border added would be dull, added unnecessary width (but could be done) so I'd consider making them P, moss or seed stitch, etc. Even a K1 bobble with one extra stitch added would add interest.
Keeping to the true form of the pattern, one would probably not do this but I'm sure it could be done, widen the scarf, too should one want to do that so just make it with more stitches to start.
Over a lacy or non lacy yarn, this pattern isn't very warm but it is decorative and could be made not as wide for a belt effect around a neck - even a belt itself with sturdy yarn; Skinny scarves are now popular and patterns can be surfed.
So, a border is added horizontally this way, but a vertical border could be added ,too. I've got a baby 'ghan and two scarves here now in knit drop stitch. Picking up the stitches on the side is very doable is knitting. One could give it a picot knit stitch, etc.
So, this would be made after the item was completed and is not a horizontal adding of extra stitches but goes vertically on the edge after picking up stitches.
I made the 'ghan very wide, turning the other way, the drops aren't vertical but appear horizontal across. One can make this drop stitch scarf running horizontally, too by throwing on 140 stitches or so and doing the same.
Sure, a crochet edge would work, too.
I'm still waiting for her to describe how she had trouble with the edge stitches, too. She didn't indicate what trouble she had (knitting). I can't imagine what trouble she had as it's just a K1, I believe.
e.ridenh: I don't see how you can do a border on the rows where the stitches have dropped. I made a scarf using "lasso" stitch, a twisted drop stitch, and there's no way you could do a border on it. You could probably crochet around the edges when you were through, but it would take several crochet stitches in each drop.