We have gathered near-infrared zyJ-band high-resolution spectra of nearly 300 field red giant stars with known lithium abundances in order to survey their HeI{lambda}10830 absorption strengths. This transition is an indicator of chromospheric activity and/or mass loss in red giants. The majority of stars in our sample reside in the red clump or red horizontal branch based on their V-J, M_V_ color-magnitude diagram, and Gaia Teff and log(g) values. Most of our target stars are Li-poor in the sense of having normally low Li abundances, defined here as log {epsilon}(Li)<1.25. Over 90% of these Li-poor stars have weak {lambda}10830 features. However, more than half of the 83 Li-rich stars (log{epsilon}(Li)>1.25) have strong {lambda}10830 absorptions. These large {lambda}10830 lines signal excess chromospheric activity in Li-rich stars; there is almost no indication of significant mass loss. The Li-rich giants may also have a higher binary fraction than Li-poor stars, based on their astrometric data. It appears likely that both residence on the horizontal branch and present or past binary interaction play roles in the significant Li-He connection established in this survey.