  Let $R$ be a lattice ordered ring along with a truncation in the sense of
Ball. We give a necessary and sufficient condition on $R$ for its unitization
$R\oplus\mathbb{Q}$ to be again a lattice ordered ring. Also, we shall see that
$R\oplus\mathbb{Q}$ is a lattice ordered ring for at most one truncation.
Particular attention will be paid to the Archimedean case. More precisely, we
shall identify the unique truncation on an Archimedean $\ell$-ring $R$ which
makes $R\oplus\mathbb{Q}$ into a lattice ordered ring.
