Newly calculated radiative transition probabilities for the A /sup 1/..sigma../sup +/ ..-->.. X /sup 1/..sigma../sup +/ (v' -v'') emission bands of /sup 7/LiH re used to calculate the radiative lifetime of the various vibrational levels (0 < or = v' < or = 26) of A /sup 1/..sigma../sup +/ LiH. For higher levels, an estimate of the bound-to-free emission probability is also needed and included. For the highest two levels, A /sup 1/..sigma../sup +/ ..-->.. B /sup 1/PI emission is possible and has been included, but makes a negligible contribution to the radiative lifetime. The calculated radiative lifetimes increase with v' from 28.9 nsec at v' = 0 to 36.1 nsec at v' = 16 and then decrease to 27.1 nsec at v' = 26. They are found to be in good agreement with measured total lifetimes, implying the nonradiative (predissociative) lifetime for the measured levels is approximately > 10/sup -7/ seconds, in accord with simple theoretical expectations.