Expensive lace is not my area. If you feel you have very important, valuable lace, you might contact a professional lace appraiser - either a private consultant or one at an auction house. You might, for example, contact either of these two women. I do not know them, and have not worked with them, but they certainly seem to have good credentials. See what they have to say?
Also, there is a lace museum in San Jose CA, and there are other museums in San Francisco, Detroit, and I am sure other cities with large textile departments. Possibly a museum lace curator could help you? I don’t know. Google “Lace Museum”. Perhaps you could email photos?
You could email a few very close-up, clear photos to me to see if I can at least identify them for you. I, personally, am not qualified to appraise fine lace, but identification is a starting point.
Needle-run is also a type of embroidery stitch done on commercial netting. It is an “in and out” running-stitch made with a sewing needle, going over and under the holes of the netting to form designs.
Limerick lace is a specific kind of embroidered lace made in Ireland. It is made on commercial netting and utilizes both tambour stitches and needle-run stitches. These two types of embroidery stitches are used in laces from many other countries as well. i.e. Limerick lace uses tambour and needle-run stitches, but not all tambour or needle-run work is Limerick.