Disagree, but hear me out. Lace cookies and brittle are totally different. Brittle is hard and snaps into chunks, but lace cookies are crisp and light. I baked a batch recently and they have this fragile, melt away texture. Calling them brittle misses the point completely, it's like confusing cake with biscotti. The lace name fits because they look and feel delicate, like actual lace. So yeah, lace cookies is the only right term for them.
My grandma always called them oatmeal lace brittles because they crack like brittle but have holes like lace. They do snap into pieces, just in a thinner, more delicate way than peanut brittle. The brown sugar and butter mix gives them that crispness, but it's still a type of brittle to me. What do you think about that?