Single photon avalanche diode (SPAD) array sensors can increase the imaging speed for fluorescence lifetime imaging microscopy (FLIM) by transitioning from laser scanning to widefield geometries. While a SPAD camera in epi-fluorescence geometry enables widefield FLIM of fluorescently labeled samples, label-free imaging of single-cell autofluorescence is not feasible in an epi-fluorescence geometry because background fluorescence from out-of-focus features masks weak cell autofluorescence and biases lifetime measurements. Here, we address this problem by integrating the SPAD camera in a light sheet illumination geometry to achieve optical sectioning and limit out-of-focus contributions, enabling fast label-free FLIM of single-cell NAD(P)H autofluorescence. The feasibility of this NAD(P)H light sheet FLIM system was confirmed with time-course imaging of metabolic perturbations in pancreas cancer cells with 10 s integration times, and in vivo NAD(P)H light sheet FLIM was demonstrated with live neutrophil imaging in a zebrafish tail wound, also with 10 s integration times. Finally, the theoretical and practical imaging speeds for NAD(P)H FLIM were compared across laser scanning and light sheet geometries, indicating a 30X to 6X frame rate advantage for the light sheet compared to the laser scanning geometry. This light sheet system provides faster frame rates for 3D NAD(P)H FLIM for live cell imaging applications such as monitoring single cell metabolism and immune cell migration throughout an entire living organism.