  Globular cluster stars show chemical abundance patterns typical of hot-CNO
processing. Lithium is easily destroyed by proton capture in stellar
environments, so its abundance may be crucial to discriminate among different
models proposed to account for multiple populations. In order to reproduce the
observed O-Na anticorrelation and other patterns typical of multiple
populations, the formation of second generation stars must occur from the
nuclearly processed stellar ejecta, responsible of the chemical anomalies,
diluted with pristine gas having the composition of first generation stars. The
lithium abundance in the unprocessed gas -which is very likely to be equal to
the lithium abundance emerging from the Big Bang- affects the lithium chemical
patterns among the cluster stars. This paper focuses on a scenario in which
processed gas is provided by asymptotic giant branch (AGB) stars. We examine
the predictions of this scenario for the lithium abundances of multiple
populations. We study the role of the non-negligible lithium abundance in the
ejecta of massive AGB (A(Li)~2), and, at the same time, we explore how our
models can constrain the extremely large ---and very model dependent--- lithium
yields predicted by recent super--AGB models. We show that the super--AGB
yields may be tested by examining the lithium abundances in a large set of blue
main sequence stars in wCen and/or NGC2808. In addition, we examine the
different model results obtained by assuming for the pristine gas either the
Big Bang abundance predicted by the standard models (A(Li)=2.6-2.7), or the
abundance detected at the surface of population II stars (A(Li)=2.2-2.3). Once
a chemical model is well constrained, the O--Li distribution could perhaps be
used to shed light on the primordial lithium abundance.
