  We examine the $\Lambda$-${}^4\mathrm{He}$ ($\alpha$) momentum correlation in
high-energy collisions to elucidate the interaction between Lambdas ($\Lambda$)
and nucleons ($N$). We compare phenomenological $\Lambda\alpha$ potentials with
different strengths at short range. In addition to the conventional
Gaussian-type potentials, we construct the $\Lambda\alpha$ potentials by
substituting the nucleon density distribution in $\alpha$ into the Skyrme-type
$\Lambda$ potentials. We find that the dependence on the employed potential
models is visible in the correlation functions from a small-size source. This
indicates that the $\Lambda\alpha$ momentum correlation could constrain the
property of the $\Lambda N$ interaction at high densities, which is expected to
play an essential role in dense nuclear matter. Also, we verify that the
Lednicky-Lyuboshits formula can yield erroneous results for a small-size source
with a potential which has a large interaction range, like the $\Lambda\alpha$
system.
