The give-away is the seam on the corners. Were it crochet she could have just continued the pattern around. Sadly, sewing gets the short shift of all the fabric arts. People don’t often give it the respect it’s due, but just look at the die cut around the bottom piece, especially the way she has it wrap the corner. Now realize how thin that fabric is and how much it must have moved under her scissor as she worked. That takes some real skill to do that.

Of course, to her generation, it wouldn’t have been “fabric art.” It was just what you did when you made a handkerchief, or a baptismal gown, or a whatever.

“Using a sock weight yarn and size 1 needles cast on 72 stitches. Join, being careful not to twist.

Cuff.
Row 1: Knit 2 Purl 2.
Repeat row 1 until cuff measures 2 inches from start.

Leg
Row 1: Knit.

Repeat row 1 until leg measures 5 inches from cuff/7 inches from cast on edge.

Heel
You will begin working back and forth on half the stitches (36).
Row 1: *Slip 1. Knit 1. Repeat from * across.
Row 2: Slip 1. Purl across”

You get the idea. This was normal. This was what people were expected to know how to do.

There are some rules in place, even for lace. If you know what you’re doing you can break them, but for knitting you normally want to lean your decreases away from your yarn overs, so “K2Tog YO” or “YO SSK”. For crochet you chain and skip stitches, so there are no decreases to lean.

Sc chain 1. Skip next sc. Sc in following sc. If you want a bigger hole, you chain a longer chain.

Sc chain 5. Skip next sc. Sc in following sc gives a long dip.
Sc. Chain 19. Skip next 5 sc. Sc in following (sixth) sc. Gives more of a long oval. And when you’ve done it enough times you can picture what’s going to happen.

After that, it’s basic math. If you do two yarn overs, you have increased 2 stitches. You must decrease 2 in order for it to work out. You want about half of your decreases to learn one way and half to lean the other or your garment will lean one way or the other. You can use that for effect, to spiral a pattern around a sock for example.

It looks to me like what you have there is some of her sewn work. The center looks, at least from the picture, like it’s woven not crocheted. The lace portion shows seam lines radiating diagonally from the square, and that’s not a normal feature of crochet. Look at your own granny squares and you’ll see what I mean. The lace work itself looks a lot like tatted lace.

That said, the lady had some mad sewing skills there. A project like that isn’t easy, especially in the bottom piece where she’s connecting the mesh to the square after cutting the shape out so perfectly. And she works it out perfectly with no puckering and extremely tiny stitches. The corners where the lace meets are perfectly mitered. Clearly, she was a woman of remarkable ability, not just with a crochet hook, but with a needle and thread as well. These are fabulous.