In this study, the Best Estimate Plus Uncertainty (BEPU) approach is developed for the systematic quantification and propagation of uncertainties in the modelling and simulation of lead-cooled fast reactors (LFRs) and applied to the demonstration LFR (DLFR) initially investigated by Westinghouse. The impact of nuclear data uncertainties based on ENDF/B-VII.0 covariances is quantified on lattice level using the generalized perturbation theory implemented with the Monte Carlo code Serpent and the deterministic code PERSENT of the Argonne Reactor Computational (ARC) suite. The quantities of interest are the main eigenvalue and selected reactivity coefficients such as Doppler, radial expansion, and fuel/clad/coolant density coefficients. These uncertainties are then propagated through safety analysis, carried out using the MiniSAS code, following the stochastic sampling approach in DAKOTA. An unprotected transient overpower (UTOP) scenario is considered to assess the effect of input uncertainties on safety parameters such as peak fuel and clad temperatures. It is found that in steady state, the multiplication factor shows the most sensitivity to perturbations in 235U fission, 235U ν, and 238U capture cross sections. The uncertainties of 239Pu and 238U capture cross sections become more significant as the fuel is irradiated. The covariance of various reactivity feedback coefficients is constructed by tracing back to common uncertainty contributors (i.e., nuclide-reaction pairs), including 238U inelastic, 238U capture, and 239Pu capture cross sections. It is also observed that nuclear data uncertainty propagates to uncertainty on peak clad and fuel temperatures of 28.5 K and 70.0 K, respectively. Such uncertainties do not impose per se threat to the integrity of the fuel rod; however, they sum to other sources of uncertainties in verifying the compliance of the assumed safety margins, suggesting the developed BEPU method necessary to provide one of the required insights on the impact of uncertainties on core safety characteristics.