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We continue our study on the hypergeometric system $E(3,6)$ which describesperiod integrals of the double cover family of K3 surfaces. Near certainspecial boundary points in the moduli space of the K3 surfaces, we constructthe local solutions and determine the so-called mirror maps expressing them interms of genus two theta functions. These mirror maps are the K3 analogues ofthe elliptic $\lambda$-function. We find that there are two non-isomorphicdefinitions of the lambda functions corresponding to a flip in the modulispace. We also discuss mirror symmetry for the double cover K3 surfaces andtheir higher dimensional generalizations. A follow up paper will describe moredetails of the latter.

K3 surfaces from configurations of six lines in $\mathbb{P}^{2}$ and mirror symmetry II --- $\lambda_{K3}$-functions ---