For simply connected nilpotent Lie groups G, we show that limit laws of infinitesimal triangular systems Delta of symmetric probability measures on G are infinitely divisible even if Delta is not commutative. The same holds also if the measures of Delta are supported by some fixed discrete subgroup Gamma subset of G. Furthermore, we give a weakening of Wehn's conditions for the accompanying laws theorem in the case of discrete subgroups of exponential Lie groups.