The mergers of binary neutron stars, as well as black hole-neutron star systems, are expected to produce an electromagnetic counterpart that can be analyzed to infer the element synthesis that occurred in these events. We investigate one source of uncertainties pertinent to lanthanide-rich outflows: the nuclear inputs to rapid neutron capture nucleosynthesis calculations. We begin by examining thirty-two different combinations of nuclear inputs: eight mass models, two types of spontaneous fission rates, and two types of fission daughter product distributions. We find that such nuclear physics uncertainties typically generate at least one order of magnitude uncertainty in key quantities such as the nuclear heating (one and a half orders of magnitude at one day post-merger), the bolometric luminosity (one order of magnitude at five days post-merger), and the inferred mass of material from the bolometric luminosity (factor of eight when considering the eight to ten days region). Since particular nuclear processes are critical for determining the electromagnetic signal, we provide tables of key nuclei undergoing β-decay, α-decay, and spontaneous fission important for heating at different times, identifying decays that are common among the many nuclear input combinations