  The surface lithium abundance A(Li) of warm metal-poor dwarf stars exhibits a
narrow plateau down to [Fe/H]~-2.8 dex, while at lower metallicities the
average value drops by 0.3 dex with a significant star-by-star scatter (called
lithium meltdown). This behaviour is in conflict with predictions of standard
stellar evolution models calculated with the initial A(Li) provided by the
standard Big Bang nucleosynthesis. The lower red giant branch (LRGB) stars
provide a complementary tool to understand the initial A(Li) distribution in
metal-poor stars. We have collected a sample of high-resolution spectra of 58
LRGB stars spanning a range of [Fe/H] between ~ -7.0 dex and ~ -1.3 dex. The
LRGB stars display an A(Li) distribution clearly different from that of the
dwarfs, without signatures of a meltdown and with two distinct components: (a)
a thin A(Li) plateau with an average A(Li)=1.09+-0.01 dex (sigma=0.07 dex), and
(b) a small fraction of Li-poor stars with A(Li) lower than ~0.7 dex. The A(Li)
distribution observed in LRGB stars can be reconciled with an initial abundance
close to the cosmological value, by including an additional chemical element
transport in stellar evolution models. The required efficiency of this
transport allows us to match also the Spite plateau lithium abundance measured
in the dwarfs. The emerging scenario is that all metal-poor stars formed with
the same initial A(Li) but those that are likely the product of coalescence or
that experienced binary mass transfer and show lower A(Li) . We conclude that
A(Li) in LRGB stars is qualitatively compatible with the cosmological A(Li)
value and that the meltdown observed in dwarf stars does not reflect a real
drop of the abundance at birth.
