  Measuring the properties of the cold neutral medium (CNM) in low-metallicity
galaxies provides insight into heating and cooling mechanisms in early
Universe-like environments. We report detections of two localized atomic
neutral hydrogen (HI) absorption features in NGC 6822, a low-metallicity (0.2
Z$_{\odot}$) dwarf galaxy in the Local Group. These are the first unambiguous
CNM detections in a low-metallicity dwarf galaxy outside the Magellanic Clouds.
The Local Group L-Band Survey (LGLBS) enabled these detections due to its high
spatial (15 pc for HI emission) and spectral (0.4 \kms) resolution. We
introduce LGLBS and describe a custom pipeline to search for HI absorption at
high angular resolution and extract associated HI emission. A detailed Gaussian
decomposition and radiative transfer analysis of the NGC 6822 detections
reveals five CNM components, with key properties: a mean spin temperature of
32$\pm$6 K, a mean CNM column density of 3.1$\times$10$^{20}$ cm$^{-2}$, and
CNM mass fractions of 0.33 and 0.12 for the two sightlines. Stacking
non-detections does not reveal low-level signals below our median optical depth
sensitivity of 0.05. One detection intercepts a star-forming region, with the
HI absorption profile encompassing the CO (2$-$1) emission, indicating
coincident molecular gas and a depression in high-resolution HI emission. We
also analyze a nearby sightline with deep, narrow HI self-absorption dips,
where the background warm neutral medium is attenuated by intervening CNM. The
association of CNM, CO, and H$\alpha$ emissions suggests a close link between
the colder, denser HI phase and star formation in NGC 6822.
