Pic plays the role of $\operatorname{End}(A)$

$\operatorname{Pic}$ for a K3 surface plays a similar role as $\operatorname{End}(A)$ for an abelian variety $A$.

$$\operatorname{Pic}(A)/\operatorname{Pic}^0(A) = \operatorname{NS}(A)$$

$\rho(A):=\operatorname{rk}(\operatorname{Pic}(A)/\operatorname{Pic}^0(A))$; also after base change.

$$\bigl(\operatorname{Pic}(A)/\operatorname{Pic}^0(A)\bigr)_{\Bbb{Q}} \simeq \{\phi \in \operatorname{End}(A)_{\Bbb{Q}} : \phi^{\dagger} = \phi\}, \qquad \dagger\text{ the Rosati involution}$$

"Compute the Picard lattice of a K3 surface" ↭ "compute $\operatorname{End}(A)$".
We also stratify moduli of abelian varieties via $\operatorname{End}(A)$.
$A$ an abelian surface, $\operatorname{char}k\neq2$ $\Rightarrow$ $\rho(\operatorname{Kum}(A)^{\mathrm{al}}) = \rho(A^{\mathrm{al}})+16$.
$\operatorname{Kum}(A)$ is the K3 surface obtained by resolving $A/\{\pm1\}$.