For those who love hand made lace.
I hunted around the forum a little bit and didn't find a direct definition of lace. We know it when we see it. It ranges from Hardanger to bobbin - torchon to Alencon - to needlelace and tatting, drawnwork, Tenerife circles, doilies and Irish crochet, which was invented (I have read) to imitate heavy Venetian lace that one book says is reminiscent of carved ivory. Then there is appliqued lace such as Isle of Wight and Carrickmacross. Lace, a textile, and filigree, which is rigid, are closely related visually.
If I dropped some strings loosely on an ironing board and ironed them so they stuck together at the overlapping points, that would be lacy in effect but it would not be lace. There has to be some structure in the design. See "Not Lace" picture below. Some is abstract, some pictorial, some naturalistic, some stylized.
Net, though highly structured, is not lace either, but it's a relative - a precursor, because embroidered net is lace, and many laces have inset sections of net or a net-like arrangement of brides, or use a fine hexagonal net as a base. Filet crochet imitates net. The lacet pattern more nearly approximates lace, but it is dubious that a solid block or border of it would constitute lace. Complex tesselations are like fancy net patterns. And what about macrame?