A five-dimensional interpolation method and corresponding computer program are developed for using published calculations to determine the non-LTE correction NLTE to the lithium abundance (Li) log derived from the Li I 6707.8 Å line. The NLTE ∆ values is determined from the following five parameters: NLTE the effective temperature T eff , the acceleration of gravity logg, the metallicity index [Fe/H], the microturbulent velocity V t , and the LTE Li abundance logε(Li) . The program is used to calculate values of ∆ and the non-LTE Li abundance for 91 single bright giants from the list of Lebre, et al. By combining these results with data for 55 stars from the previous paper, we obtain the non-LTE values of logε(Li) for 146 FGK-giants and supergiants. We confirm that, because of the absence of the Li line in the spectra of most of these stars, it is only possible to estimate for them an upper limit for the Li abundance. A large spread is confirmed in logε(Li) for stars with masses M ≤6M . A comparison of these results with model calculations of stars confirms the unique sensitivity of the lithium abundance to the initial rotation velocity V 0 . We discuss the giants and supergiants with lithium abundances log ε(Li) = 1.4 ± 0.3, which could have a rotation velocity V 0 =0 km/s and have already undergone deep convective mixing. Li-rich giants with lithium abundances logε(Li) ≥2 and nearly up to the initial value of log ε(Li) = 3.2 ± 0.1 are examined. It is shown that the fraction of Li-rich giants with V 0 ≈ 0 − 50 km/ s is consistent with current evolu-tionary models. The other stars of this type, as well as all of the "super Li-rich" giants, for which the standard theory is untenable, can be explained by invoking the hypothesis of recent lithium synthesis in the star or an alternative hypothesis according to which a giant planet is engulfed by the star.