I made a pattern for the collar to this chemise. In fact I made about four of them. This one fitted the best. I basted it in the neckline, arranged the lace on a half of it and marked the outline according to it.
According to the pattern I got, I cut two collars, the lower was cut on the bias and sewed from two halves, the upper was cut normally and had fusible interfacing ironed on.
I folded the seam allowance in and ironed. That wasn't necessary at the lower collar..
You already know the principals of pinning in quarters:-)
Each arch was divided in thirds, I drew them on the collar with chalk.
I sewed the pleats with a sewing thread instead of the basting one, I'll let those stitches there inside the collar.
The lace has been carefully ironed.
I had to make the corners in the lace. I sewed them diagonally..
..cut the allowance and pressed flat..
..zig-zag stitched and draged the threads under the stitches.
I finished the whole lace. I turned it inside and put the lower collar on the upper one (right sides together). I sewed in the seamline, except for the corners, then I turned it over and sewed the corners in hand.
I cut the lower collar in the neckline edge a bit more than the upper one was.
That made the final shape of the collar, it shouldn't be flat. I arranged the neckline edges to the same level and sewed them together so that the stitches would stay in the seam allowance.