  For a natural number $m$, a Lie algebra $L$ over a field $k$ is said to be of
breadth type $(0, m)$ if the co-dimension of the centralizer of every
non-central element is of dimension $m$. In this article, we classify finite
dimensional nilpotent Lie algebras of breadth type $(0, 3)$ over $\mathbb F_q$
of odd characteristics up to isomorphism. We also give a partial classification
of the same over finite fields of even characteristic, $\mathbb C$ and $\mathbb
R$. We also discuss $2$-step nilpotent Camina Lie algebras.
