Dlsyn,

A solid divider might work, but it would have to be deep (a foot or so) to deter all but the deepest probing roots. Those old-fashioned daylilies are vigorous, to say the least. I have 'Kwanso' (the double form of the plain orange native) and I have to pull errant fans every summer. They come out easily after a rain. Mine don't seem to travel DEEP so much as FAR, so if I had that problem in my yard I'd go for a foot-deep solid divider, but I don't know what material I'd use. To be perfectly solid, that could be fun to find. Heavy plastic sheeting or a tarp, folded to several thicknesses and laid vertically in a narrow trench then backfilled, might be the most economical route, especially for a longer stretch to block.

Laurel

Look for the root barrier products sold by companies to contain bamboo, such as the one here:

http://www.burtonsbamboogarden.com/catalog/index.php?sel_category=5