According to molecular orbital theory Li2+ has 5 electrons −σ1s2σ∗1s2σ2s1
Li2− has 7 electrons −σ1s2σ∗1s2σ2s2σ∗2s1
bondorder=2electroninbondingmolecularorbital−ElectroninAntibondingmolecularorbital
Bond order of Li2+=23−2=21
Bond order of Li2−=24−3=21
As both have similar bond order, both Li2+ and Li2− will be stable.
Note: Li2− will be relatively unstable to Li2+ as it has more electrons in anti bonding orbitals, so have more energy and having more repulsion so Li2− is less stable as Li2+