In order to shed light on hypertriton lifetime puzzle, we will measure the hypertriton lifetime in time domain directly as an independent and complementary approach from heavy-ion experiments. We employ the (K$^-$, $\pi^0$) reaction to populate hypertriton using a K$^-$ beam at J-PARC. By detecting a high-energy gamma-ray decaying from $\pi^0$ at forward angle, this reaction can be tagged efficiently. We newly developed PbF$_2$ calorimeter and the performance was evaluated with positron and hadron beams. We found that the energy resolution is $\sigma$/E = 5.0 %/$\sqrt{\rm{E/GeV}}$, which is sufficient for the high-energy gamma-ray tagging in our experiment.