This unusual shape is taken from a silver ingot, a tradable currency during the Ming and Qing dynasties. This shape appears in early lacquerwares, cf. a Song dynasty mother-of-pearl inlaid box from the Asian art Museum of San Francisco, illustrated in Hai-Wai Yi-Chen, Chinese Art in Overseas Collections, Lacquerware, Taiwan 1987, p.39
For a very similar four-tiered lacquer box from the Ming dynasty, see Lacquer Wares of the Yuan and Ming Dynasties - The Complete Collection of Treasures of the Palace Museum, Hong Kong 2006, pl.82. Although the shape is different from the current example, the foot rim and sides are very much alike.