  We have determined precise stellar parameters and lithium abundances in a
sample of 117 stars with basic properties very similar to the Sun. This sample
selection reduces biasing effects and systematic errors in the analysis. We
estimate the ages of our sample stars mainly from isochrone fitting but also
from measurements of rotation period and X-ray luminosity and test the
connection between lithium abundance, age, and stellar parameters. We find
strong evidence for increasing lithium depletion with age. Our sample includes
14 stars that are known to host planets and it does not support recent claims
that planet-host stars have experienced more lithium depletion than stars
without planets. We find the solar lithium abundance normal for a star of its
age, mass, and metallicity. Furthermore, we analyze published data for 82 stars
that were reported to support an enhanced lithium depletion in planet hosts. We
show that those stars in fact follow an age trend very similar to that found
with our sample and that the presence of giant planets is not related to low
lithium abundances. Finally, we discuss the systematic biases that led to the
incorrect conclusion of an enhanced lithium depletion in planet-host stars.
