We present a pointfree generalization of outer measures by replacing $\mathcal{P}(X)$ with a bounded distributive lattice $L$, studying functions $\mu: L\to [0,\infty]$ satisfying lattice-theoretic versions of outer measure axioms (null-preserving, monotone, $\sigma$-subadditive). For such an outer measure, we introduce $\mu$-measurable elements via a generalized Carath'eodory condition and show that they form a sublattice closed under complements. When $L$ is a Boolean $\sigma$-frame, the collection $\mathcal{M}_\mu$ of measurable elements is itself a Boolean $\sigma$-frame; counterexamples demonstrate the necessity of the Boolean hypothesis for closure under countable joins. Moreover, for any $\sigma$-frame $L$ (without requiring the Boolean condition), the restriction of $\mu$ to $\mathcal{M}_\mu$ is $\sigma$-additive. We also examine the categorical behavior of the assignment $\mu \mapsto \mathcal{M}_\mu$, which yields a natural transformation between suitable functors, and pose an open question: whether every Boolean $\sigma$-subframe of $L$ arises as $\mathcal{M}_\mu$ for some outer measure $\mu$. This work extends classical measure theory to pointfree settings, revealing fundamental connections between order-theoretic, measure-theoretic, and categorical structures.