In many fields of life science, visualization of spatial proximity, as an indicator of protein interactions in living cells, is of outstanding interest. A method to accomplish this is the measurement of Förster resonant energy transfer (FRET) by means of spectrally resolved fluorescence lifetime imaging microscopy. The fluorescence lifetime is calculated using a multiple-wavelength fitting routine. The donor profile is assumed first to have a monoexponential time-dependent behavior, and the acceptor decay profile is solved analytically. Later, the donor profile is assumed to have a two-exponential time-dependent behavior and the acceptor decay profile is derived analytically. We develop and apply a multispectral fluorescence lifetime imaging microscopy analysis system for FRET global analysis with time-resolved and spectrally resolved techniques, including information from donor and acceptor channels in contrast to using just a limited spectral data set from one detector only and a model accounting only for the donor signal. This analysis is used to demonstrate close vicinity of β-secretase (BACE) and GGA1, two proteins involved in Alzheimer's disease pathology. We attempt to verify if an improvement in calculating the donor lifetimes could be achieved when time-resolved and spectrally resolved techniques are simultaneously incorporated.