Fitting of the fluorescence lifetimes for fluorophores can be achieved using various techniques. Problems arise when the fluorophore sample itself is heterogeneous and the fluorescence decay is far from exponential, as a single sample may have a distribution of lifetimes. We study the fitting of fluorescence lifetimes for two systems, a homogeneous and near-exponential fluorescein dye and a highly heterogeneous system of graphene quantum dots. We fit a variety of different models to experimental time-correlated single photon counting fluorescence data from each system, evaluating the validity of each model for the two systems. We find that, for the near-exponential system, there is little difference between the fit of each model. However, for strongly nonexponential behavior, the models give quite different estimates of mean and standard deviation, indicating that appropriate model choice and assessment is crucial in obtaining meaningful lifetimes from fluorescence lifetime data. Moreover, we perform simulation studies that strengthen these conclusions.