  Let $X$ be a finite connected poset and $K$ a field. We study the question,
when all Lie automorphisms of the incidence algebra $I(X,K)$ are proper.
Without any restriction on the length of $X$ we find only a sufficient
condition involving certain equivalence relation on the set of maximal chains
of $X$. For some classes of posets of length one, such as finite connected
crownless posets (i.e., without weak crown subposets), crowns and ordinal sums
of two antichains we give a complete answer.
