  Lusztig \cite{L5,L6} gave a parametrization for $\rm{Irr}(G^F)$, where $G$ is
a reductive algebraic group defined over $\mathbb{F}_q$, with Frobenius map
$F$. This parametrization is known as Lusztig's Jordan decomposition or Lusztig
correspondence. However, there is not a canonical choice of Lusztig
correspondence. In this paper, we consider classical groups. We pick a
canonical choice of Lusztig correspondence which is compatible with parabolic
induction and is compatible with theta correspondence. This result extends
Pan's result in \cite{P3}. As an application, we give a refinement of the
results of the finite Gan-Gross-Prasad problem in \cite{Wang1} and prove a
duality between Theta correspondence and finite Gan-Gross-Prasad problem, which
can be regarded as a finite field instance of relative Langlands duality of
Ben-Zvi-Sakellaridis-Venkatesh \cite{BZSV}.
