Exploring thermoelectric materials with captivating chemical bonding and low lattice thermal conductivity (kappa(l)) is crucial in thermoelectric research. Here, we propose two-dimensional (2D) gamma-monochalcogenide (MX; M = Ge, Sn, Pb, and X = S, Se, Te) monolayers as potential thermoelectric materials. The exfoliation energies of gamma-MX monolayers fall in the 12-16 meV/A(2) range, less than graphene (21 meV/A(2)), suggesting their feasible realization through mechanical or chemical exfoliation. The electronic band structures exhibit an indirect band gap ranging from 0.41 eV for gamma-PbTe to 0.86 eV for gamma-PbS. The metavalent bonding in these monolayers results in an unusual trend in kappa(l) with atomic mass. Among studied monolayers, the gamma-PbTe monolayer exhibits an ultralow room temperature kappa(l) of 0.49 W/mK, which accounts for its increased anharmonicity and higher scattering rates from acoustic and low-lying optical phonons. Despite having a higher mass than gamma-PbS, gamma-PbSe demonstrates enhanced kappa(l) values. Similar anomalous behavior is observed in the case of gamma-GeTe (8.57 W/mK), gamma-GeSe (3.10 W/mK), gamma-SnTe (4.30 W/mK), and gamma-SnSe (3.31 W/mK) monolayers. The enhanced kappa(l) in tellurides is attributed to the high bond stiffness, low charge transfer between M and X atoms, and widening of the phonon gap, which significantly reduces the phonon scattering. The above anomalies observed in kappa(l) originate in the unique bonding mechanism (metavalent bonding), which suppresses the conventional reductive effect of mass to define kappa(l). Our findings elucidate the distinct thermal transport properties of 2D materials and provide valuable insights for designing efficient thermoelectric materials.