Ask Mr. Smarty Plants

There are five species of native plants in our Native Plant Database that have a common name that includes "Lily of the Valley".  They are:

Convallaria majuscula (American lily of the valley)  and the USDA Plants Database distribution map

Maianthemum dilatatum (False lily of the valley) and the USDA Plants Database distribution map

Maianthemum racemosum (Feathery false lily of the valley) and the USDA Plants Database distribution map

Maianthemum stellatum (Starry false lily of the valley) and the USDA Plants Database distribution map

Maianthemum trifolium (Threeleaf false lily of the valley) and the USDA Plants Database distribution map

If you check out the distribution maps for each of them, you will see that only one of them (Maianthemum racemomusum, Feathery false lily of the valley) is shown as occurring in Texas.  If you click on Texas on that distribution map you will see that its occurrence is in West Texas far from Red River County.  However, if you click on Oklahoma on that distribution map, you will see it is shown as occurring in McCurtain County, Oklahoma which is adjacent to Red River County, Texas; so, it is entirely possible that species could occur naturally there.

Although the distribution map for Maianthemum stellatum (Starry false lily of the valley) doesn't show it occurring in Texas, it does show it occurring both in Oklahoma and Arkansas. However, on neither distribution map for either of the two states does the occurrence of the species fall near Red River County, Texas.

My guess is that the more likely reason that you saw it there is because someone bought a Lily of the Valley plant, perhaps as a memorial tribute, and planted it there.   Convallaria majalis (European lily of the valley) is one non-native species that is sold commercially and is recommended for USDA Plant Hardiness Zones 2 - 8.  Red River County is at the northern edge of Zone 8 (8a) so this imported Lily of the Valley could survive there.