on the Here-Be-Tatters yahoo email group, there has been a discussion of Lattice Tatting.
I am posting here 4 scans of Lattice style tatting from Julia E Sanders book Tatting Patterns.
Collar page 16
Detail of Collar pg 17
Doily pg 19
detail of doily pg 18~~later~~ I got to thinking that while I didn't have the lattice snowflake anymore, there might be another project in my UFO stash. so here is a project that I was working on many a year ago, put aside for some reason and never finished.

Looks like I will have to finish it this winter after I have gotten Christmas items and other sewing projects finished.
There is no pattern for this, if I remember correctly, it was a way to practice mignonette stitch and I liked the look of the Lattice; just something I was working on at the time. I used very tiny joining picots to make the Lattice here, but I have done it with alligator joins. I will have to put a 4th round of some kind on this as I didn't join the outer rings to each other. hhhmmm wonder what I should use....