  Standard Big Bang nucleosynthesis at baryonic density as inferred by WMAP
implies a primordial Li7 abundance factor of two to three larger than that
inferred by observations of low--metallicity halo stars. Recent observations of
Li6 in halo stars suggest a pre--galactic origin of this isotope, which is
exceedingly difficult to explain by putative high redshift cosmic ray
populations. We investigate if one or both of these lithium problems may be
solved by late decaying relic particles in the Constrained Minimal
Supersymmetric Standard Model (CMSSM) coupled to gravity. Assuming that the
gravitino is the lightest supersymmetric particle (LSP) we find that in large
parts of the CMSSM parameter space either of these problems can be potentially
solved. In particular, we also find solutions where both lithium problems may
be solved simultaneously. These entail the hadronic decay of relic 1 TeV staus
into 100 GeV gravitinos at 1000 sec after the Big Bang, as proposed by one of
us before. Moreover, the produced gravitinos naturally contribute a large
fraction, or all, to the by WMAP required dark matter density. A prediction of
this model is the dark matter to be lukewarm with free--streaming lengths of
the order of a 4 keV early freezing--out relic particle. Such lukewarm
gravitino dark matter may have beneficial effects to the formation of galactic
structures and may be constrained by the reionisation history of the Universe.
The current version of the paper presents results for both cases (a) when
catalytic nuclear reations are included and (b) when they are neglected.
