On the Log Abundance for Compact {K{ä}hler} threefolds II

In this article we show that if $(X, \Delta)$ is a log canonical compact Kähler threefold pair such that $K_X+\Delta$ is nef and the numerical dimension $\nu(X, K_X+\Delta)=2$, then $K_X+\Delta$ is semi-ample. This result combined with our previous work in arXiv:2201.01202 shows that the log abundance holds for log canonical compact Kähler threefold pairs.