  Let $G$ be a simple undirected graph.A broadcast on $G$ isa function $f :
V(G) \to \mathbf{N}$ such that $f(v)\le e_G(v)$ holds for every vertex $v$ of
$G$, where $e_G(v)$ denotes the eccentricity of $v$ in $G$, that is, the
maximum distance from $v$ to any other vertex of $G$.The cost of $f$ is the
value cost$(f)=\sum_{v\in V(G)}f(v)$.A broadcast $f$ on $G$ is independent if
for every two distinct vertices $u$ and $v$ in $G$,
$d_G(u,v)>\max\{f(u),f(v)\}$,where $d_G(u,v)$ denotes the distance between $u$
and $v$ in $G$.The broadcast independence number of $G$ is then defined as the
maximum cost of an independent broadcast on $G$.A caterpillar is a tree such
that, after the removal of all leaf vertices, the remaining graph is a
non-empty path.A lobster is a tree such that, after the removal of all leaf
vertices, the remaining graph is a caterpillar.In [M. Ahmane, I. Bouchemakh and
E. Sopena.On the Broadcast Independence Number of Caterpillars.Discrete Applied
Mathematics, in press (2018)], we studied independent broadcasts of
caterpillars.In this paper, carrying on with this line of research, we consider
independent broadcasts of lobsters and give an explicit formula for the
broadcast independence number of a family of lobsters called locally uniform
$2$-lobsters.
