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Based on an 𝑒+𝑒− collision data sample corresponding to an integrated luminosity of 567 pb−1 taken at the center-of-mass energy of √𝑠=4.6 GeV with the BESIII detector, we measure the absolute branching fraction of the inclusive decay Λ+𝑐→Λ+𝑋 to be ℬ(Λ+𝑐→Λ+𝑋)=(38.2+2.8−2.2±0.9)% 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 𝒜𝐶𝑃≡[ℬ(Λ+𝑐→Λ+𝑋)−ℬ(¯Λ−𝑐 → ¯Λ+𝑋)]/[ℬ(Λ+𝑐→Λ+𝑋)+ℬ(¯Λ−𝑐 → ¯Λ+𝑋)]=(2.1+7.0−6.6±1.6)%, a statistically limited result with no evidence of 𝐶𝑃 violation.