I used the straight punch (not the corner piece) from the Double Loops Punch Around the Page set by Martha Stewart Crafts.
Continue to punch across the strip, lining it up with the guide image on the punch as usual.
Now, turn the strip around and insert the uncut edge into the punch (see below). This time line up the same starting edge of the paper, but only with the mark on the opposite side of the punch. As shown in the image below.
Carefully punch across the strip making sure to line it up with the guide image on the punch as you go.
You'll end up with a lacey strip that you can use on your projects! You could make multiple strips and lay them near each other to create a block of lace or to replicate the look of lace cut cardstock.
Here is a card I made with the lace strip in the example above.
I also tried this technique with the Doily Lace edge punch also by Martha Stewart Crafts. This is one of my favorite punches when I'm card making.
Since this punch doesn't have markings on the sides, I instead used a mark on the guide image for lining up the paper when I punched it. This punch design is also a little bit deeper than the loops punch, so I increased my paper strip width to 1.25". Here is the result that I got.