Answer
The proposed decay conserves the strangeness.
Work Step by Step
The $\Lambda^0$ strangeness is $-1$
The $p$ strangeness is $0$
The $K^-$ strangeness is $-1$
The strangeness on the left side of the decay is $-1$
The net strangeness on the right side of the decay is $-1$
Therefore, the proposed decay conserves the strangeness.
