A wide-field microscope with epi-fluorescence and selective plane illumination was combined with a single-photon avalanche diode (SPAD) array camera to enable live-cell fluorescence lifetime imaging (FLIM) using time-correlated single-photon counting (TCSPC). The camera sensor comprised of 192×128\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {192}\ imes \ ext {128}$$\\end{document} pixels, each integrating a single SPAD and a time-to-digital converter. Jointly, they produced a stream of single-photon images of photon arrival times with ≈38 ps\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\approx \ ext {38 ps}$$\\end{document} accuracy. The photon arrival times were subject to systematic delays and nonlinearities, which were corrected by a Monte-Carlo algorithm. The SPAD camera was then applied to FLIM where histogramming the resulting photon arrival times in each pixel resulted in decays compatible with common data processing pipelines for fluorescence lifetime analysis. The capabilities of the TCSPC camera-based FLIM microscope were demonstrated by imaging living unicellular photosynthetic algae and artificial lipid vesicles. Epi-fluorescence illumination enabled rapid fluorescence lifetime imaging of living cells and selective-plane illumination enabled 3-dimensional FLIM of stationary samples.