The investigation of thermal properties of recently emerged two-dimensional (2D) materials is a necessary step towards fulfilling their potential applications in nano-electronics devices. In this study, the thermal conductivity of novel \b{eta}-NX (X=P, As, Sb) monolayers are investigated using a first-principles density functional theory (DFT) study based on the full solution of the linearized Peierls-Boltzmann transport equation (PBTE). The results show that the room temperature thermal conductivities of \b{eta}-NP, \b{eta}-NAs, and \b{eta}-NSb are about 1.1, 5.5, and 34.0 times higher than those of single-element \b{eta}-P, \b{eta}-As, and \b{eta}-Sb monolayers, respectively. The phonon transport analysis reveals that higher phonon group velocities as well as phonon lifetimes are responsible for such an enhancement in the lattice thermal conductivities of \b{eta}-NX (X=P, As, Sb) binary compounds compared to single-element group-VA monolayers. We found that \b{eta}-NP has the minimum thermal conductivity among \b{eta}-NX (X=P, As, Sb) monolayers, while it has the minimum average atomic mass, which is in contrast with the common assumption that lower mass systems exhibit higher thermal conductivities. This work demonstrates the trade-off between harmonic and anharmonic phonon properties in determining the variation of the thermal conductivity among \b{eta}-NX (X=P, As, Sb) monolayers. The higher anharmonicity in \b{eta}-NP is found to be responsible for the lower thermal conductivity of this monolayer.