  In this work, we propose a possible assignment of the newly observed
$X(2239)$, as well as the $\eta(2225)$, as a molecular state from the
interaction of a baryon $\Lambda$ and an antibaryon $\bar{\Lambda}$. With the
help of effective Lagrangians, the $\Lambda\bar{\Lambda}$ interaction is
described within the one-boson-exchange model with $\eta$, $\eta'$, $\omega$,
$\phi$, and $\sigma$ exchanges considered. After inserting the potential kernel
into the quasipotential Bethe-Salpeter equation, the bound states from the
$\Lambda\bar{\Lambda}$ interaction can be studied by searching for the pole of
the scattering amplitude. Two loosely bound states with spin parities
$I^G(J^{PC})=0^+(0^{-+})$ and $0^-(1^{--})$ appear near the threshold almost
with the same parameter. The $0^-(1^{--})$ state can be assigned to the
$X(2239)$ observed at BESIII, which is very close to the $\Lambda\bar{\Lambda}$
threshold. The scalar meson $\eta(2225)$ can be interpreted as a $0^+(0^{-+})$
state from the $\Lambda\bar{\Lambda}$ interaction. The annihilation effect is
also discussed through a coupled-channel calculation plus a phenomenological
optical potential. It provides large widths to two bound states produced from
the $\Lambda\bar{\Lambda}$ interaction. The mass of the $1^-$ state is a little
larger than the mass of the $0^-$ state after including the annihilation
effect, which is consistent with our assignment of these two states as
$X(2239)$ and $\eta(2225)$, respectively. The results suggest that further
investigation is expected to understand the structures near the
$\Lambda\bar{\Lambda}$ threshold, such as $X(2239)$, $\eta(2225)$, and
$X(2175)$.
