The electronic structure of Li-doped Ni$_{1-x}$Fe$_x$O has been investigated using photoemission spectroscopy (PES) and x-ray absorption spectroscopy (XAS). The Ni $2p$ core-level PES and XAS spectra were not changed by Li doping. In contrast, the Fe$^{3+}$ intensity increased with Li doping relative to the Fe$^{2+}$ intensity. However, the increase of Fe$^{3+}$ is only $sim 5%$ of the doped Li content, suggesting that most of the doped holes enter the O $2p$ and/or the charge-transferred configuration Ni $3d^8underline{L}$. The Fe 3d partial density of states and the host valence-band emission near valence-band maximum increased with Li content, consistent with the increase of electrical conductivity. Based on these findings, percolation of bound magnetic polarons is proposed as an origin of the ferromagnetic behavior.