I did a quick search on your plant and it looks like your plant can be split by just the root system. Looks as every root may produce another entire plant. Also it looks like it can be propagated by hardwood, softwood cuttings and by saving the seeds.

Usually any plant will produce seeds where the bloom is. You can do this by letting the bloom fade completely and then where the bloom head was will be where the seed will produce. The best way to tell if the seed is ripe is that where the seed head is underneath will actually begin to turn brown.

Though I am not sure where you are located at but I noticed that while searching for your plant that many states regard silver lace as invasive and will choke out any surrounding plants.

Here is a link that might be useful: Search results for