The ${}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.28em}{0ex}}\phantom{\rule{1.0pt}{0ex}}4}$H bound state and the $S$-wave hypertriton(${}_{\ensuremath{\Lambda}}^{\phantom{\rule{0.16em}{0ex}}3}$H)-$\ensuremath{\Lambda}$ scattering in spin singlet and triplet channels below the hypertriton breakup momentum scale are studied in halo/cluster effective field theory at leading order by treating the ${}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.28em}{0ex}}\phantom{\rule{1.0pt}{0ex}}4}$H system as a three-cluster ($\ensuremath{\Lambda}$-$\ensuremath{\Lambda}$-deuteron) system. In the spin singlet channel, the amplitude is insensitive to the cutoff parameter ${\ensuremath{\Lambda}}_{c}$ introduced in the integral equation, and we find that there is no bound state. In this case, the scattering length of the hypertriton-$\ensuremath{\Lambda}$ scattering is found to be ${a}_{0}^{}=16.0\ifmmode\pm\else\textpm\fi{}3.0$ fm. In the spin triplet channel, however, the amplitude obtained by the coupled integral equations is sensitive to ${\ensuremath{\Lambda}}_{c}$, and we introduce the three-body contact interaction ${g}_{1}^{}({\ensuremath{\Lambda}}_{c})$. After phenomenologically fixing ${g}_{1}^{}({\ensuremath{\Lambda}}_{c})$, we find that the correlation between the two-$\ensuremath{\Lambda}$ separation energy ${B}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}$ from the ${}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.28em}{0ex}}\phantom{\rule{1.0pt}{0ex}}4}$H bound state and the scattering length ${a}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{}$ of the $S$-wave $\ensuremath{\Lambda}$-$\ensuremath{\Lambda}$ scattering is significantly sensitive to the value of ${\ensuremath{\Lambda}}_{c}$.