  Recent spectroscopic observations of metal poor stars have indicated that
both $^7$Li and $^6$Li have abundance plateaus with respect to the metallicity.
Abundances of $^7$Li are about a factor three lower than the primordial
abundance predicted by standard big-bang nucleosynthesis (SBBN), and $^6$Li
abundances are $\sim 1/20$ of $^7$Li, whereas SBBN predicts negligible amounts
of $^6$Li compared to the detected level. These discrepancies suggest that
$^6$Li has another cosmological or Galactic origin than the SBBN. Furthermore,
it would appear that $^7$Li (and also $^6$Li) has been depleted from its
primordial abundance by some post-BBN processes. In this paper we study the
possibility that the radiative decay of long-lived particles has affected the
cosmological lithium abundances. We calculate the non-thermal nucleosynthesis
associated with the radiative decay and explore the allowed region of the
parameters specifying the properties of long-lived particles. We also impose
constraints from observations of the CMB energy spectrum. We find that
non-thermal nucleosynthesis produces $^6$Li at the level detected in metal poor
halo stars (MPHSs), when the lifetime of the unstable particles is of the order
$\sim 10^8-10^{12}$~s and their initial abundance with respect to that of the
photons is $\sim (10^{-13}-10^{-12}~{\rm GeV})/E_{\gamma 0}$, where $E_{\gamma
0}$ is the emitted photon energy in the radiative decay. We conclude that the
most likely nucleosynthetic scenario involves two different processes. First, a
non-thermal cosmological nucleosynthesis associated with the radiative decay of
unstable particles; and second, the stellar depletion of both of the primordial
lithium isotopic abundances.
