  We have measured stellar parameters, [Fe/H], lithium abundances, rotation,
and 12C/13C in a small sample of red giants in three open clusters that are
each home to a red giant star that hosts a substellar companion (NGC2423 3,
NGC4349 127, and BD+12 1917 in M67). Our goal is to explore whether the
presence of substellar companions influences the Li content. Both 12C/13C and
stellar rotation are measured as additional tracers of stellar mixing. One of
the companion hosts, NGC2423 3, is found to be Li-rich with A(Li)_NLTE=1.56
dex, and this abundance is significantly higher than the A(Li) of the two
comparison stars in NGC2423. All three substellar companion hosts have the
highest A(Li) and 12C/13C when compared to the control red giants in their
respective clusters; however, except for NGC2423 3, at least one control star
has similarly high abundances within the uncertainties. Higher A(Li) could
suggest that the formation or presence of planets plays a role in the degree of
internal mixing on or before the red giant branch. However, a multitude of
factors affect A(Li) during the red giant phase, and when the abundances of our
sample are compared to abundances of red giants in other open clusters
available in the literature, we find that they all fall well within a much
larger distribution of A(Li) and 12C/13C. Thus, even the high Li in NGC2423 3
cannot be concretely tied to the presence of the substellar companion.
