Answer:
Calculating the photon lifetime of a distributed Bragg reflector cavity is possible in OptiFDTD. The transverse mode properties of the cavity can readily be calculated using OptiMode, which is included with OptiFDTD. The confinement factor can also be evaluated with the toolbox included.
For the leakage and photon lifetime, it can be determined from monitoring the radiated fields at the output facets versus the total field emitted. You will have to perform some simple post processing on data generated by OptiFDTD.