Based on observed far-infrared properties of K giant stars, we propose
a scenario linking the high Li abundances of some of these stars to t
he evolution of circumstellar shells. In this model, every K giant wit
h masses between 1.0 and 2.5 M. become Li rich during the red giant br
anch stage, and the internal mechanism responsible for the Li enrichme
nt will initiate a prompt mass-loss event. The evolutionary paths of t
he detached shells are compatible with observations for low expansion
velocities of the order of 2 km s(-1) and mass loss of (2-5) x 10(-8)
M. yr(-1). This modest mass loss is, however, 2 orders of magnitude la
rger than those of normal, Li-poor K giants. A ''Li time'' of the orde
r of 80,000 yr or somewhat larger is possible. This Li phase is, never
theless, not related to the C-12/C-13 ratio which appears to evolve, f
or these low-mass stars, over a much longer time. This model requires
a rapid internal process of Li enrichment and depletion. New arguments
appearing in the literature concerning this internal process are disc
ussed. Reference is also made to the importance of these stars to the
Galactic Li evolution.