In [Kar, Purkait and Sarkar, Birkhoff center of c-semiring, Asian-Europ. J. Math. 12(1) (2019) 1950003, 11 pp.], Kar et al. introduced the notion of Birkhoff center of a c-semiring and obtained some characterizations of this center. In this paper, we study different types of lattice structures of Birkhoff center of a c-semiring. We also prove that if two c-semirings are isomorphic, then their Birkhoff centers are isomorphic but the converse is not necessarily true.