Lower-tropospheric stability (LTS) regulates convective boundary-layer growth, low-cloud evolution, pollutant dispersion, and land–atmosphere coupling, yet continuous observations are scarce because thermodynamic profilers are sparse and expensive, and reanalysis products explain less than one-third of the observed variance in inversion strength even at well-instrumented sites. We retrieve continuous LTS at the Atmospheric Radiation Measurement Southern Great Plains observatory from routine surface-flux measurements and Doppler-lidar-derived mixed-layer height, using a regime-aware, stage-partitioned framework established in earlier work. At the central facility over May 2016–December 2020 the retrieval reproduces observed LTS with a coefficient of determination of 0.78 and a mean absolute error of 2.39 K, and captures the full diurnal evolution of stability. The principal contribution is a diagnostic for judging when such a retrieval can be transferred to another site. Predictor-distribution differences, quantified by the Kullback–Leibler divergence, are weighted by SHapley Additive exPlanations sensitivities to form a single metric, ΔKL×|SHAP|. Applied to two extended facilities, the metric shows that distributional differences degrade transferability only where the retrieval is sensitive to the shifted predictor, and identifies cloud-base height, mixed-layer height, and thermodynamic predictors as the dominant contributors at the poorer-performing site. Gaussian perturbation experiments provide an independent fingerprint: monotonic error growth indicates a transferable relationship limited by random observational uncertainty, whereas a non-monotonic response indicates structural thermodynamic mismatch. Requiring only predictor distributions and model sensitivities, the diagnostic applies to any data-driven atmospheric retrieval.