  A finitely generated group is lacunary hyperbolic if one of its asymptotic
cones is an $\mathbb{R}$-tree. In this article we give a necessary and
sufficient condition on lacunary hyperbolic groups in order to be stable under
free product by giving a dynamical characterization of lacunary hyperbolic
groups. Also we studied limits of elementary subgroups as subgroups of lacunary
hperbolic groups and characterized them. Given any countable collection of
increasing union of elementary groups we show that there exists a lacunary
hyperbolic group whose set of all maximal subgroups is the given collection. As
a consequence we construct a finitely generated divisible group. First such
example was constructed by V. Guba in \cite{Gu86}. In section 5 we show that
given any finitely generated group $Q$ and a non elementary hyperbolic group
$H$, there exists a short exact sequence $1\rightarrow N\rightarrow
G\rightarrow Q\rightarrow 1$, where $G$ is a lacunary hyperbolic group and $N$
is a non elementary quotient of $H$. Our method allows to recover \cite[Theorem
3]{AS14}. In section 6, we extend the class of groups
$\mathcal{R}ip_{\mathcal{T}}(Q)$ considered in \cite{CDK19} and hence give more
new examples of property $(T)$ von Neumann algebras which have maximal von
Neumann subalgebras without property $(T)$.
