  A mass paucity of compact objects in the range of $\sim 2-5 ~M_\odot$ has
been suggested by X-ray binary observations, namely, the "lower mass gap".
Gravitational wave detections have unlocked another mass measurement method,
and aLIGO/Virgo has observed some candidates in the gap. We revisit the
numerical simulations on the core-collapse supernovae (CCSNe) for $\sim
20-40~M_\odot$ progenitor stars with differently initial explosion energies. As
a result, the lower explosion energy naturally causes more efficient fallback
accretion for low-metallicity progenitors, and then the newborn black holes
(BHs) in the center of the CCSNe can escape from the gap, but neutron stars
cannot easily collapse into BHs in the gap; nevertheless, the final remnants of
the solar-metallicity progenitors stick to the gap. If we consider that only
drastic CCSNe can be observed and that those with lower explosion energies are
universal, the lower mass gap can be reasonably built. The width and depth of
the gap are mainly determined by the typical CCSN initial explosion energy and
metallicity. One can expect that the future multi-messenger observations of
compact objects delineate the shape of the gap, which might constrain the
properties of the CCSNe and their progenitors.
