  We present an analysis of Li abundances in low mass stars (LMS) during the
Red Giant Branch (RGB) and Asymptotic Giant Branch (AGB) stages, based on a new
determination of their luminosities and evolutionary status. By applying
recently suggested models for extra-mixing, induced by magnetic buoyancy, we
show that both Li-rich and Li-poor stars can be accounted for. The simplest
scenario implies the development of fast instabilities on the RGB, where Li is
produced. When the fields increase in strength, buoyancy slows down and Li is
destroyed. 3He is consumed, at variable rates. The process continues on the
AGB, where however moderate mass circulation rates have little effect on Li due
to the short time available. O-rich and C-rich stars show different histories
of Li production/destruction, possibly indicative of different masses. More
complex transport schemes are allowed by magnetic buoyancy, with larger effects
on Li, but most normal LMS seem to show only the range of Li variation
discussed here.
