  Based on an $e^+e^-$ collision data sample corresponding to an integrated
luminosity of 567$\,\rm{pb}^{-1}$ taken at the center-of-mass energy of
$\sqrt{s} = 4.6$ GeV with the BESIII detector, we measure the absolute
branching fraction of the inclusive decay $\Lambda_{c}^{+} \to \Lambda + X$ to
be $\mathcal{B}(\Lambda_{c}^{+} \to \Lambda + X)=(38.2^{+2.8}_{-2.2}\pm0.8)\%$
using the double-tag method, where $X$ refers to any possible final state
particles. In addition, we search for direct CP violation in the charge
asymmetry of this inclusive decay for the first time, and obtain
$\mathcal{A}_{CP} \equiv \frac{\mathcal{B}(\Lambda_{c}^{+} \to \Lambda +
X)-\mathcal{B}(\bar{\Lambda}_{c}^{-} \to \bar{\Lambda} +
X)}{\mathcal{B}(\Lambda_{c}^{+} \to \Lambda +
X)+\mathcal{B}(\bar{\Lambda}_{c}^{-} \to \bar{\Lambda} + X)} =
(2.1^{+7.0}_{-6.6}\pm1.4)\%$, a statistically limited result with no evidence
of CP violation.
