  This paper is a continuation of the recent work of Guo-Xiang-Zheng
\cite{Guo-Xiang-Zheng-2021-CV}. We deduce sharp Morrey regularity theory for
weak solutions to the fourth order nonhomogeneous Lamm-Rivi\`ere equation
\begin{equation*} \Delta^{2}u=\Delta(V\nabla u)+div(w\nabla
u)+(\nabla\omega+F)\cdot\nabla u+f\qquad\text{in }B^{4},\end{equation*} under
smallest regularity assumptions of $V,w,\omega, F$ and that $f$ belongs to some
Morrey spaces, which was motivated by many geometrical problems such as the
flow of biharmonic mappings. Our results deepens the $L^p$ type regularity
theory of \cite{Guo-Xiang-Zheng-2021-CV}, and generalizes the work of Du, Kang
and Wang \cite{Du-Kang-Wang-2022} on a second order problem to our fourth order
problems.
