  The four-point correlation function is the lowest order correlation function
for scalar fields that can be used to probe statistical parity invariance in an
isotropic universe. There are intriguing claims of detection of parity
violation in the 4-point function of BOSS galaxy clustering data. We apply the
same estimator to the public SDSS Data Release 16 Lyman-$\alpha$ forest data.
Lyman-$\alpha$ forest data probes a different redshift range and is sensitive
to a different density regime using a completely different technique. A
detection would therefore be a strong indication of new physics. We identify
accurate covariance matrix as a crucial impediment to performing this
measurement accurately, consistent with existing literature on galaxy 4-point
function. We discuss several approaches to estimating the covariance matrix,
several of which produce spurious detection. Using a robust, but very
suboptimal, covariance matrix derived from subsample bootstrapping, we find no
evidence for parity violation.
