Rydberg state lifetimes in the singly ionized lithium atom were calculated using an inward integration approach and a Hartree-Slater potential to represent the ionic core. The calculated oscillator strengths for the s-p and p-d transitions compare favorably with high accuracy calculations using Hylleraas-type wavefunctions for the limited number of states for which such results are available. Comparison with the also sparse experimental studies of lifetimes is good overall and our predictions indicate specific revisions of some experimental determinations. The effects due to black-body radiation were explicitly included, but found to be insignificant for the states with n < 11, even at temperatures of 600 K.