We report on detailed calculations of high-order harmonic generation (HHG) spectra from Li, Li+, and He using the Lewenstein model. Our model well describes the HHG experiment in Li plasma [J. Phys. B45, 065601 (2012)JPAPEH0953-407510.1088/0953-4075/45/6/065601]. The cutoff position, in the case of neutral lithium atoms (43th harmonic of 800nm radiation), corresponds to 3.5×1014 W/cm2 laser intensity, as numerically-simulated in the current work. The difference from the experimental value can be well explained by the measurement errors and uncertainty in determining the laser intensity, which is usually around 25%. We found that Li+ ions do not contribute to HHG plateau region of the spectra and that those ions start to contribute only at very high intensities. Our calculations show that the application of materials possessing higher ionization potential does not necessarily leads to the extension of HHG cutoff.