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High lithium-7 ($\mathrm{^7Li}$) abundances in giants are indicative ofnon-standard physical processes affecting the star. Mechanisms that couldproduce this signature include contamination from an external source, such asplanets, or internal production and subsequent mixing to the stellar surface.However, distinguishing between different families of solutions has provenchallenging, and there is no current consensus model that explains all thedata. The lithium-6 ($\mathrm{^6Li}$) abundance may be a potentially importantdiscriminant, as the relative $\mathrm{^6Li}$ and $\mathrm{^7Li}$ abundancesare expected to be different if the enrichment were to come from internalproduction or from engulfment. In this work, we model the $\mathrm{^6Li}$ and$\mathrm{^7Li}$ abundances of different giants after the engulfment of asubstellar mass companion. Given that $\mathrm{^6Li}$ is more strongly affectedby Galactic chemical evolution than $\mathrm{^7Li}$, $\mathrm{^6Li}$ is not agood discriminant at low metallicities, where it is expected to be low in bothstar and planet. For modeled metallicities ([Fe/H]$>-0.5$), we use a "bestcase" initial $\mathrm{^6Li/^7Li}$ ratio equal to the solar value.$\mathrm{^6Li}$ increases significantly after the engulfment of a companion.However, at metallicities close to solar and higher, the $\mathrm{^6Li}$ signaldoes not last long in the stellar surface. As such, detection of surface$\mathrm{^6Li}$ in metal-rich red giants would most likely indicate the actionof a mechanism for $\mathrm{^6Li}$-enrichment other than planet engulfment. Atthe same time, $\mathrm{^6Li}$ should not be used to reject the hypothesis ofengulfment in a $\mathrm{^7Li}$-enriched giant or to support a particular$\mathrm{^7Li}$-enhancement mechanism.

On Lithium-6 as diagnostic of the lithium-enrichment mechanism in red giants