Bulk gallium oxide (Ga2O3) has been widely used in lasers, dielectric coatings for solar cells, deep-ultraviolet transistor applications due to the large band gap over 4.5 eV. With the miniaturization of electronic devices, atomically thin Ga2O3 monolayer has been unveiled recently, which features an asymmetric configuration with a quintuple-layer atomic structure. The superior stability, the strain-tunable electronic properties, high carrier mobility and optical absorption indicate the promising applications in the electronic and photoelectronic devices. However, the strict investigation of lattice thermal conductivity (kappa_L) of 2D Ga2O3 is still lacking, which has impeded the widespread use in practical applications. Here, we report the computational discovery of low kappa_L with a value of 10.28 W m-1 K-1 at 300 K in atomically thin Ga2O3. Unexpectedly, two quasi-acoustic shear phonon modes contribute as high as 27% to the kappa_L at 300 K, leading to 37% contribution of optical phonon modes, much larger than many other 2D materials. We also find that the quasi-acoustic shear mode can emerge in the system without van der Waals interactions. This work provides new insight into the nature of thermal transport in non-van der Waals monolayer materials and predicts a new low kappa_L material of potential interest for thermal insulation in transistor applications.