  Planetary engulfment events have long been proposed as a lithium (Li)
enrichment mechanism contributing to the population of Li-rich giants (A(Li) >=
1.5 dex). Using MESA stellar models and A(Li) abundance measurements obtained
by the GALAH survey, we calculate the strength and observability of the surface
Li enrichment signature produced by the engulfment of a hot Jupiter (HJ). We
consider solar-metallicity stars in the mass range of 1-2 $\mathrm{M_\odot}$
and the Li supplied by a HJ of 1.0 $\mathrm{M_J}$. We explore engulfment events
that occur near the main sequence turn-off (MSTO) and out to orbital
separations of 0.1 AU. We map our results onto the Hertzsprung-Russell Diagram,
revealing the statistical significance and survival time of lithium enrichment.
We identify the parameter space of masses and evolutionary phases where the
engulfment of a HJ can lead to Li enrichment signatures at a $5\sigma$
confidence level and with meteoritic abundance strengths. The most compelling
strengths and survival times of engulfment-derived Li enrichment are found
among host stars of 1.4 $\mathrm{M_\odot}$ near the MSTO. Our calculations
indicate that planetary engulfment is not a viable enrichment pathway for stars
that have evolved beyond the subgiant branch. For these sources, observed Li
enhancements are likely to be produced by other mechanisms, such as the
Cameron-Fowler process or the accretion of material from an asymptotic giant
branch (AGB) companion. Our results do not account for second-order effects,
such as extra mixing processes, which can further dilute Li enrichment
signatures.
