Let $K$ be a field of positive characteristic $p$ and $KG$ the group algebra of a group $G$. It is known that, if $KG$ is Lie nilpotent, then its upper (or lower) Lie nilpotency index is at most $|G'|+1$, where $|G'|$ is the order of the commutator subgroup. Previously we determined the groups $G$ for which the upper/lower nilpotency index is maximal or the upper nilpotency index is `almost maximal' (that is, of the next highest possible value, namely $|G'|-p +2$). Here we determine the groups for which the lower nilpotency index is `almost maximal'.