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Traditional Hessenstickerei, sometimes confused with Schwälmer Stickerei, is a texture bound whitework with elements of "cutwork", achieved by pulling threads out of the fabric.
A machine done FSL Crochet design (folk art style) inserted to a linen will imitate the look best.
If you are looking for lace bags, Embroidery Library has some nice ones. Not free however. Search the FSL sections
if you google images for hessian bags...you will see they look sort of like sack material...closer weaved then burlap...but simular...you can get an idea of what she wants...this sitehttp://bejoscha.tavernmaker.de/DE... has free designs...and one is of a lace bag...too cute...perhaps that would do...