Lithium-rich red giants have been a long-standing mystery in stellar astrophysics. A leading theory to explain these chemically peculiar and rare objects is interactions with a close companion. To investigate their companion fraction, we collected high-resolution spectra of 33 Li-rich red giants using ESPRESSO, and used The Joker constrain their orbital parameters. We find an overall companion rate of (9/33). Secondary masses reveal one planetary companion (), three brown dwarfs (), and five stellar-mass companions (). Our findings suggest that Li-rich red giants with lower lithium abundance () tend to be in binaries as compared to those with higher lithium abundance, and Li-rich red giants with have a higher companion rate than those outside of this range. We offer two potential formation mechanisms of our Li-rich sample: (i) the progenitor mass of stellar mass companions suggest that these objects were potentially lithium-producing, intermediate-mass AGB stars; (ii) the sub-stellar companions were initially in multi-planet systems, but dynamical instability caused the tidal dissipation of close-in planets thereby enhancing the red giant in lithium. Extended baselines and dedicated follow-up with Gaia DR4 astrometry are required to confirm the orbital parameters of our systems and distinguish between mechanisms.

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