The decision to sell or keep our family's old collections is purely personal. Sometimes just the association with a beloved family member is enough to create a sentimental value. Sometimes, the love of a particular collection (or single item) is a good reason to maintain ownership. The best reasons to sell or get rid of the old stuff is if you don't really care for it; if you are trying to downsize; or would prefer the money over the item.
You can learn more about the lanterns in a book like "Classic Lanterns: A Guide and Reference" by Dennis A. Pearson for Schiffer Books for Collectors or "Collectible Lanterns Including Household, Barn, and Railroad Lanterns" by L & W Books.
If you can't decide what to do with the lanterns why not just keep them around for a while until you can decide. After research, you may want to keep one or two for sentimental value.