By a K3 fibered Calabi-Yau threefold, I mean a smooth projective threefold $X$ with trivial canonical class and $h^{1,0}(X) =h^{2,0}(X) = 0$ that has a fibration $X \rightarrow \mathbb P^1$ whose generic fibers are smooth K3 surfaces (to be denoted by $S_X$)

I gathered some examples of mirror pairs of those K3-fibered CY threefolds.

Borcea--Voisin CY's,

CY double coverings over some quasi-Fano threefolds in this paper.

From these examples, I observed:

In these examples of mirror pairs of K3-fibered CY threefolds X, Y. Their generic K3 fibers are K3 mirrors (in the definition of this paper). In concrete words, there are embeddings lattices $\phi_X: Pic(S_X) \rightarrow L$, $\phi_Y: Pic(S_Y) \rightarrow L$ to K3 lattice $L$ of rank 22 and signature $(3, 19)$ such that $L = im(\phi_X) \oplus im(\phi_Y) \oplus U$ ,where $U$ is a unimodular hyperbolic plane in $L$.

My question is:

- Are there other examples of mirror pairs of K3-fibered CY threefolds that support or fail this observation.

- If other known examples also support this observation, Is this observation expected from any kind of theories of mirror symmetry of Calabi-Yau threefolds with K3 fibration?