Answer
See the answer below.
Work Step by Step
$Li_2^+$ has one valence electron and $Li_2^-$ has three, so the configuration is respectively:
$[core]\ (\sigma_{2s})^1$
$[core]\ (\sigma_{2s})^2\ (\sigma_{2s}^*)^1$
Since $B.O.=(N.\ Bonding -N.\ Antibonding)/2$
These ions have a bond order of 0.5 thus having a weaker bond than $Li_2$ with a bond order of 1.