Good Morning, and thanks for reaching out!

Lily of the Valley is a moderately aggressive spreading plant - using rhizomes to propagate underground. It is listed as native in some sources, and non-native in others. Given the proper conditions it will spread and push out other species, which based on your message is not a concern here. Its root systems do however, lend itself to fighting erosion.

For future reference, I've included sources helpful in determining what is invasive and what isn't - (including what characteristics put a plant on this list). The first is specific to Vermont and includes a list of officially recognized invasives, as well as a watch list. The second has a wider scope in N. America and lets you explore where a certain plant is identified as invasive.

Lily of the Valley looks to be listed as invasive in Wisconsin and Alaska, but is not listed in Vermont law or invasive lists. It is a vigorous grower, so if used, care should be taken in determining whether it has the possibility to invade other areas and choke out other plants.

Gallery of Terrestrial Plants | Vermont Invasives (vtinvasives.org)

lily of the valley, Convallaria majalis Liliales: Liliaceae (invasive.org)