Answer
This process can proceed via the strong interaction.
Work Step by Step
The $K^-$ has strangeness $-1$
The proton $p$ has strangeness $0$
The $\Lambda^0$ has strangeness $-1$
The $\pi^0$ has strangeness $0$
The net strangeness of the left side of the process is $-1$
The net strangeness of the right side of the process is $-1$
Since strangeness is conserved in this process, this process can proceed via the strong interaction.
