  For $c\geq 2$, the free centre-by-(nilpotent-of-class-c-1)-by abelian Lie
ring on a set $X$ is the quotient $L/[(L')^c,L]$ where $L$ is the free Lie ring
on $X$, and $(L')^c$ denotes the $c$th term of the lower central series of the
derived ideal $L'=L^2$ of $L$. In this paper we give a complete description of
the torsion subgroup of its additive group in the case where $|X|=2$ and $c$ is
a prime number.
