First-principle predictions of inclusive heavy-particle decay is key to interpreting experimental data and testing the Standard Model. However, lattice QCD data requires ill-posed analytic continuation before such predictions can be made. Bergamaschi, it et al. proposed using Nevanlinna-Pick interpolation to address this inverse problem which provides rigorous bounds on the continued results. We propose a precise method to incorporate the uncertainty inherent in lattice data in this interpolation. The combined lattice and interpolation errors for the simplified example studied are statistically well-controlled and suggest that ab initio lattice methods may be applied to these inclusive processes.