how to calculate recombination lifetime for holes for a specific diode?
Correct me if I am wrong but wouldn't calculating \$t_p\$ 
use the following symbolic rearrangement?

$$t_p = \frac{t_{sd}}{\ln\left(1+ \frac{\text{Final forward current}}{\text{generator reverse current}}\right)}$$

(I can't read your picture very well so I could actually be REALLY wrong)

If that is the equation then that would lead me to conclude that it would depend on the specific circuit setup each time? Due to the fact that the natural log number would actually change. This would mean there is no "standard data sheet number" to compare to?

That and the data sheet wasnt very helpful (http://www.diodes.com/_files/datasheets/ds28002.pdf)