  We prove that any holomorphic function $f$ on the Lie ball of even dimension
satisfying $\Delta f=0$ is obtained uniquely by the higher-dimensional Penrose
transform of a Dolbeault cohomology for a twisted line bundle of a certain
domain of the Grassmannian of isotropic subspaces. To overcome the difficulties
arising from that the line bundle parameter is outside the {\it{good range}},
we use some techniques from algebraic representation theory.
