  The Lane-Emden system is written as \begin{equation*} \begin{cases} -\Delta u
= v^p &\text{in } \Omega,\\ -\Delta v = u^q &\text{in } \Omega,\\ u, v > 0
&\text{in } \Omega,\\ u = v = 0 &\text{on } \partial \Omega \end{cases}
\end{equation*} where $\Omega$ is a smooth bounded domain in the Euclidean
space $\mathbb{R}^n$ for $n \ge 3$ and $0< p< q <\infty$. The asymptotic
behavior of least energy solutions near the critical hyperbola was studied by
Guerra \cite{G} when $p \geq 1$ and the domain is convex. In this paper, we
cover all the remaining cases $p < 1$ and extend the results to any smooth
bounded domain.
