is Li ion less stable than Li atom?
What do you mean by "stable"? In a vacuum, $\ce{Li+}$ is quite stable. In water, Li ionizes readily to $\ce{Li+}$, with $\ce{OH-}$ accepting that electron. Of course, in vacuo, if an $\ce{Li+}$ ion were to be placed near an $\ce{Li-}$ ion, they'd quickly redistribute the charge.

There is also a difference between chemical (thermodynamic) stability and kinetic stability. Lifting a ball up a hill, or lifting an electron to a higher level, gives it potential energy, but if the ball rests in a cup on the hill, or the electron is in a metastable state, it will not go back on its own without a push.

Thermoluminescence is a case in point. Over time, some materials such as ceramics absorb radiation from cosmic sources and nearby radioactive minerals, putting atoms into excited states. Upon reheating, electrons hop back to lower states, emitting light. This is used to date ancient pottery, since the metastable states are preserved for millenia.

Another example of metastability is diamond. It takes considerable pressure and a specific temperature range to convert carbon, e.g. graphite, to diamond -- but once that pressure is removed, graphite is the preferred state. However, once formed, diamond is stable at room temperature for eons.

See Difference between thermodynamic and kinetic stability, answered by thomij, for a much more complete answer.