  We study some properties on $\mathsf{Lie}$-centroids related to central
$\mathsf{Lie}$-derivations, generalized $\mathsf{Lie}$-derivations and almost
inner $\mathsf{Lie}$-derivations. We also determine the $\mathsf{Lie}$-centroid
of the tensor product of a commutative associative algebra and a Leibniz
algebra.
