It can be done through time resolved studies. Phosphoresce has longer life time (milliseconds to microsecond) as compared to fluorescence (nanoseconds). Usually phosphorescence is not observed at room temperature and very low temperatures and oxygen free conditions are required to observe it.
if by "lifetime" you mean the lifetime of the photoluminescence signal after excitation by a short pulse, the answer is yes : phosphorescence is associated with a much longer lifetime than fluorescence, as stated by Gophal above
this ignores the possibility of "delayed fluorescence" (see the reference i gave above for a discussion) ; i have no experience with "metal complexes" so i can't give you any hint as to whether delayed fluorescence could occur or not in this kind of material
Another quick test to differentiate fluorescence from phosphorescence is oxygen quenching. Assuming your ground state is a singlet, fluorescence won't be quenched by the presence of oxygen, but phosphorescence will. If you have phosphorescence, which is pretty common in inorganic chromophores, the emission intensity (and lifetime) will decrease in the presence of oxygen.