Here is a website that I found to be quite rational and helpful for cleaning more common lace in general:
http://reallyhandmade.com/how-to-clean-antique-lace-and-other-delicate-fibers/
Here are my own personal suggestions for cleaning linens and / or lace.
With a little diligence, I usually get my antique linens and laces stain free and sparkling here at my home. I am not a professional launderer and I am very cautious. It is not difficult, and requires mostly 1.) water, 2.) time, and 3.) patience. I use an enameled canning pot.
Here is what works for me with average sturdy lace, linen tablecloths, and bed linens.
In a large bowl, tub, pot or sink make a mixture of cold water and an oxygen-based laundry product. Don’t use bleach, lemon, vinegar or any acidic cleaner. Don’t mix oxygen-based products with any other cleaning product like clorox!
Put the linen or lace in to soak. The longer it soaks, the whiter it becomes – be patient. I often leave very stained linens soaking for six days. But check every day, as sometimes it doesn't take so long. The handful of stains that are stubborn, I treat with Spray and Wash and soak a day longer.
Rinse very well – at least three different rinses, until all traces of cleaner are gone. Squeeze the water out - no wringing or twisting. Roll it in a large towel to get more of the water out. Plain, unadorned linen or cotton can go into the dryer. If it has delicate lace inserts or edging, don't chance it! Line dry, or drape it over the ironing board to dry.
I personally prefer no starch, as I like my linens to have a billowy, soft, pliable hand. If you prefer a stiffer look and feel - or if you just want to add body to a rather worn, thin, droopy set of napkins, use Niagara spray starch. Easy to use.
Caveat: Though I have been laundering linens and lace for years. I have never been able to entirely remove black ink, colored candle-wax stains, motor grease or rust stains. I steer clear of buying any linens with these stains. But the process outlined above nearly always removes pasta sauce, tea, red wine, espresso, blood. ( We Italians...ahem.. have rather wild meal times...)
And remember: A few pale yellow stains left over are not necessarily a bad thing! They attest to age and authenticity. What is the point of having antique and vintage linens if they do not show their age and history? A little worn spot, a snagged thread, a bit of missing edge lace, a tea stain or two – it is only a little added charm.