  Using the sample of 348 stars from the PennState-Torun Centre for Astronomy
Planet Search, for which uniformly determined atmospheric parameters are
available, with chemical abundances and rotational velocities presented here,
we investigate various channels of Li enrichment in giants. Our work is based
on the HET/HRS spectra. The A(Li) was determined from the 670.8nm line, while
we use a more extended set of lines for alpha-elements abundances. In a series
of K-S tests, we compare Li-rich giants with other stars in the sample. We also
use available IR photometric and kinematical data in search for evidence of
mass-loss. We investigate properties of the most Li-abundant giants in more
detail by using multi-epoch precise radial velocities. We present Li and
alpha-elements abundances, as well as vsini for 348 stars. We detected Li in 92
stars, of which 82 are giants. 11 of them show significant Li abundance
A(Li)>1.4 and 7 of them are Li-overabundant objects, according to criterion of
A(Li)>1.5 and their location on HR diagram, including two giants with Li
abundances close to meteoritic level. For another 271 stars, upper limits of
A(Li) are presented. We show that Li-rich giants are among the most massive
stars from our sample and show larger than average effective temperatures. They
are indistinguishable from the complete sample in terms of their distribution
of luminosity, [Fe/H], vsini, and alpha-elements abundances. Our results do not
point out to one specific Li enrichment mechanism operating in our sample of
giants. On the contrary, in some cases, we cannot identify fingerprints of any
of known scenarios. We show, however, that the 4 most Li-rich giant in our
sample either have low-mass companions or have RV variations at the level of
~100 m/s, which strongly suggests that the presence of companions is an
important factor in the Li-enrichment processes in giants.
