In 1863 an upstart American company called Ott & Brewer started producing a version of the Irish Belleek, and their products had marks which included the word Belleek.
Other American companies that included Belleek in their marks were the Willets Manufacturing Company, the Ceramic Art Company - which became Lenox, Morris & Willmore (Columbian Art Pottery Co.), From what I can find, the word Belleek was no longer used in American wares after 1930.
The box and ashtray are in fantastic condition and looks to be hardly used, if at all.
In the early 20th century, separate dining rooms and hostess parties became the trendy thing to do.
Lenox became popular when they started producing custom designed, elaborate dining plates.
Shops specializing in high quality ceramic pottery carried Lenox products.
These products were displayed in the Smithsonian Institution in 1897.
Famous artists of the time were hired to design the plates.