L galeobdolon is tough, no doubt about it, and I also grow it in an area of dry shade with lots of tree roots. I enjoy it for its attractive foliage, which is also evergreen here, and the short lived but very attractive, in my experience, soft yellow flowers, which will appear soon. It does spread as mentioned in the article by long runners, which root at the nodes, but I find them easy to control (though one does have to watch where they do break,as the article mentions, but it is shallow rooted and thus not that difficult to remove those rooted node sections). One difference from the author's garden is that I have no shrubs nearby where it can insinuate itself into, so I just chop off the runners and dig any rooted sections that try to invade the more intensively planted areas around the patch that are filled with many less aggressive native and non native plants. By rigorously controlling its spread I have been able to enjoy its garden presence for several years. I agree with the author's comments about not encouraging it with more favored positions where its spreading tendencies could accelerate. It is also definitely not a plant to grow for the gardener who won't keep up with it on a regular basis or you will soon have a lawn of it. Carefully and consistantly managed, however, it is a beautiful and useful plant for difficult areas. As for the other lamiums, I grow those too, they are slower to spread but certainly are capable of it. The least likely to spread is Herman's Pride, supposedly a selection of L. galeobdolon, though I seriously doubt it, b/c its habit is so different. In fact the only thing they have in common is yellow flowers. In my garden Herman's Pride remains as a small tightly growing upright clump, without any of the surface runners of the other lamiums I grow. In areas like the PNW which have a climate that is probably very favorable for lamiums to become invasive headaches, Herman's Pride might be a better choice.
Hi Lori--I second the Herman's Pride recommendation above. In fact I wish my clumps would grow a bit faster. I've divided them to spread them around a bit.
Another dry shade lover that I highly recommend is Geranium Mac Bevan's Variety. Aside from not being invasive it has other attributes to recommend it. The leaves have a rounded shape that is decoratively notched and they release a pine fragrance at the slightest disturbance. The flowers are a beautiful lavender/magenta color. The plant forms a small colony which slowly grows in size. I started with a gallon-pot-sized plant, which has grown to about 24" in diameter in four years. It's low-growing, rarely more than 8" tall. If you'd like to check it out, you may do so here: http://www.bluestoneperennials.com/b/bp/GEBVS.html.