Lifetime analyses are crucial for ensuring the durability of new Light-emitting Diodes (LEDs) and uncertainty quantification (UQ) is necessary to quantify a lack of usable failure and degradation data. This work presents a new framework for predicting the lifetime of LEDs in terms of lumen maintenance, effectively quantifying the natural variability of lifetimes (aleatory) as well as the reducible uncertainty resulting from data scarcity (epistemic). Non-parametric survival models are employed for UQ of low-magnitude failures, while a new parametric interval prediction model (IPM) is introduced to characterize the uncertainty in high-magnitude lumen depreciation events and long-term extrapolated lifetimes. The width of interval-valued predictions reflects the inherent variability in degradation paths whilst the epistemic uncertainty, arising from data scarcity, is quantified by a statistical bound on the probability of the prediction errors for future degradation trajectories. A modified exponential flux decay model combined with the Arrhenius equation equips the IPM with physical information on the physics of LED luminous flux degradation. The framework is tested and validated on a novel database of LED degradation trajectories and in comparison to well-established probabilistic predictors. The results of this study support the validity of the proposed approach and the usefulness of the additional UQ capabilities.