There is nothing called the "Exact lifetime" of a fluorophore since it is a statistical average. It solely depends on the analysis method (expecting that you are using single photon counting), i.e. the upper and lower limit of data acquisition, the fitting algorithm used etc. It's always a range (like in between x and y ns). For BSA in aqueous buffer, the mode of decay is bi-exponential (that does not correspond to two Trp residues though, because if the bi-exponential decay correspond to two different Trp residues, we should obtain a mono-exponential decay for HSA which has only one Trp, but here also the decay is bi-exponential), with one lifetime close to 1.2 ns (we obtained 1.33 ns) and another around 6-6.5 ns (we got 6.46 ns). You can go through our article (J. Photochem. Photobiol. B, 2014, 133, 99) or some others listed in the references of the article to gain an insight. I hope this helps.

In addition to what Aniruddha already wrote, each excited-Trp residue is usually comprised of at least two different transition dipole moments, each of which is associated with a de-excitation rate and its reciprocal serves as one of this Trp lifetime components. Researchers measuring time-resolved fluorescence usually calculate some sort of a mean lifetime. They fit the Trp fluorescence decay with a sum of exponentials function, having the minimum possible exponents [Sum(ai*exp(-t/ti)); with ti being the i'th fluorescence lifetime component and ai being the associated amplitude], convoluted with the experimental IRF. Then they usually calculate some sort of a weighted mean lifetime from the best fit lifetime components and their relative amplitudes. If you are interested in calculating the mean lifetime which is relative to the mean quantum yield you usually calculate

=[Sum(ai*ti^2)] / [Sum(ai*ti)].

But if you are interested in a mean lifetime that will be proportional to the area below the fluorescence decay (for instance for FRET) you usually calculate 

=[Sum(ai*ti)] / [Sum(ai)].

All of this is good for just one Trp. In your case you have two, which might be affected (both lifetime components and their relative amplitudes) by the different residue microenvironments. If you still want to stick to using the two Trp residues of BSA, you'd better measure each Trp for the two different single Trp mutants (possibly exchanging each Trp with a Phe group, and hoping the structure, stability and function are not compromised.

Thanks  Aniruddha Ganguly and Eitan Lerner for your valuable suggestions..I appreciate a lot..