  Measuring the kaon structure beyond the proton and pion structures is one of
the hot topics in hadron physics, as it is one way to understand the nature of
Nambu-Goldstone boson of QCD and to see the interplay between the EHM mechanism
and the HB mechanism for hadron mass generation. In this paper, we present a
simulation of the leading $\Lambda$ baryon tagged deep inelastic scattering
experiment at EicC (Electron-ion collider in China), which is engaged to unveil
the internal structure of kaon through Sullivan process. According to our
simulation results, the suggested experiment will cover the kinematical domain
of $0.05\lesssim x_{\rm K} \lesssim 0.85$ and $Q^2$ up to 50 GeV$^2$, with the
acceptable statistical uncertainties. In the relatively low-$Q^2$ region ($<10$
GeV$^2$), the Monte-Carlo simulation shows a good precision of the measurement
($<5$\%) for the kaon structure function $F_2^{\rm K}$. In the high-$Q^2$
region (up to 50 GeV$^2$), the statistical uncertainty of $F_2^{\rm K}$ is also
acceptable ($<10$\%) for the data at $x_{\rm K}<0.8$. To perform such an
experiment at an electron-ion collider, a high-performance zero-degree
calorimeter is required.
